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Their ship and her payload were designed as a colony expedition. They had not just asteroid mining craft, and seeds for hydroponics, and modular habitat sections, they also had the blueprints and machine tools to replicate them. And they had the engineers to read the blueprints and use the tools.

For the stardrive, they had just the operators' maintenance handbook, and pilots and engineers trained to operate it.

Consider: You are obviously able to use a computer, like billions of people worldwide. And there are many millions who can program a simple website. But how many can design a microchip, or manufacture one? A programmer would know about silicon wafers, and doping it with other elements, but how many can explain the physics behind that?

So the colony would have to replicate a R&D project. They get a head start because they know it is possible, and also the principles how it works. This is balanced by the need to build the colony as planned. They know that they have a fleet of sublight ships, and that these sublight ships will wear out, and that they should start assembling the shipyard to build new sublight ships.

The ship consists of stages, and only the final stage arrived.

This is a very realistic explanation. That's how we build rockets, because it's efficient and much cheaper. Might not fit your plot, though. Given that they are only left with the smallest of the stages they could only guess how to build the most complex stages.

The ship carried just enough energy to arrive there, a return would have been very expensive and was not planned.

Again, this refers to the cost of interstellar travels. This should also apply to single stage vehicles. Refueling this ship would be extremely expensive, or might even be impossible due to a lack of technology or industry, see also next point.

The crew is smaller than the population of a planet.

Seriously, why would those few people be able to build a spacecraft? Imagine what an extremely complex project this would be. Remember how the soviet union struggled to put a man on moon (admittedly in a short time), because they lacked the industrial power for this huge project. They might be able to repair their ship, but build a new one? How long would it take to build up the industry? How many people can actually work on this, while there are plenty of other problems to work on?

It costs a lot of money and they lack the political will to use all those resources for that scope.

See what happened with the Apollo program. As long as USSR was leading the space race the US Congress was scared by the enemy supremacy and had no troubles providing funding to the program.

Once the Moon was reached more than once and public attention lowered, together with the manifest incapacity of the Soviet space program to replicate the result, suddenly the budget was limited and even scheduled launches were canceled.

This is similar in effect to Separatrix's unobtainium answer, but a slightly different spin.

AI created all of the FTLs in existence. No flesh and blood brain can fully comprehend the details of their inner workings enough to recreate one. This doesn't mean they don't understand the broad strokes of how it works, just that they can't replicate it.

Then the AI went to war with its creator civilization, and ultimately lost. With the AI wiped out, a ban was put in place to ensure no more AI.

This means that every FTL is a priceless, irreplaceable artifact. No more can ever be constructed (by this civilization, at least).

When the ship crashed, and the FTL drive exploded it created a anti-FTL radiation field in the system. The anti-FTL radiation prevents ships traveling at FTL speeds, by destroying the craft if it tries. After the first ship they built exploded trying to go to FTL they haven't tried again. Maybe by now the radiation has dispersed but no one wants to risk the crew/resources needed to try again.

They were never able to construct FTL drives - they got them from a forerunner factory that was still intact, which they had discovered during their own early steps into space.

(Or they purchased the FTL drive from extant aliens, or FTL tech is a particular company's closely guarded secret, etc...)

Perhaps they have tried to create a new FTL drive from remains of their old one, and it backfired so much - risked so many lives, nearly tore through the ship, messed up with their resources, etc - and leaves barely anything of the attempt that the rest simply say 'it's not worth it' and stop any further pooling of resources into making one.

When they crash-landed in the new star system, the scientists and technicians who were knowledgeable and part of producing FTL died, the computers and backups containing information on how to build/rebuild the equipment were also destroyed.

The remaining scientists and technicians have little knowledge of physics involved to produce FTL engine, and they were not property trained.

It was unfortunate for the scientists and technicians to die. There was a malfunction in the ship they were in when exiting FTL, sending the ship crashing down to the planet.

Because they are astronauts(pilots) and not engineers.

Our society is able to do many things that I alone cannot.

Some of the technology requires licensing from organizations that are not here. You may have gotten unlimited licenses for OperatingSystem2525, and all of the computers visible to crew and passengers run on that version. The software to run the engines requires OperatingSystem2530, which needs a long trip in the opposite direction to get an unlock key. And now that you've disassembled your engines to find that out, your current engines also want a new unlock key.

Many fictional FTL drives (as if there were any others..) can only be used far away from pesky gravity fields.

Your drive is the opposite: it actually needs to be spun up at the center of a sufficiently large planet to break through to the fifth dimension or whatever.

Since you incautiously blew up the only planet in reach, now you're stuck there.

Totaly running with ths' answer here. FTL drives arn't so much as a engine, so much as a trans dimensional artillery piece(T-DAP)... and Earth had to hollow out most of Pluto to build their outbound gun. Accuracy at colonization distances can reliably hit a solar system, but hitting a planet was supposed to be statistically impossible. Turns out, it wasn't impossible... and even worse, inflating a 200 KM bubble of space-time inside a planet's core tends to do really bad things it its structural integrity. Now 80% of the plant's mass is flying around the sun in wildly eliptical orbits and its going to take generations to collect enough mass to build a new T-DAP.....

The best answers are story based, and your story gives the best reason: "holy crap we crashed and destroyed a PLANET, next time it might be the ship!". Would you trust that ship? Would you get enough crazy people together for another jump to colonize something else? They could just not have the expertise or facilities to see why they crashed or repair it. They could be waiting for rescue, or trying to build enough of a population and facilities to research and build a new FTL drive even if it takes a few millenia to redo that research.

The other more standard answers are already given. Lack of resources for the FTL drive (either building or fueling), lack of reasons to build them (you reached a starsystem right?), lack of economical insentive to build/use the ship (cost of FTL is so high only a colonist expedition is worth it, but why waste resources on something that wont earn your local system something?)

Structural Damage

During the crash some important parts of the FTL engine have been damaged or destroyed. Repairing them is not (easily) possible. Maybe they just don't have the plans required for a certain part. Maybe they lack a certain ressource that is absolutely needed to form a certain part of the engine. Maybe certain parts need a giant machinery to be produced that can't simply be reproduced from existing ressources.

Side effects

They were a test drive of a new FTL engine that had an unwelcome sideeffect of killing or heavily hurting the people on board. To extend their lives, they rather don't restart the engine. This might also not have been an initial issue, but caused by the crash that destroyed some protectors that can't be reinstalled with available ressources

Escape

Your ship is controlled by rebels that are on their escape from an evil empire. They found a reasonably well suited habitat. They might be able to restart their FTL in an emergency but would rather stay at their current place and try to establish their rebel empire. A couple of generations and propaganda later nobody remembers the fact that they were even capable of FTL travel.

That's going to depend on exactly what your FTL drive needs.

How about processing power equivalent to an Intel I7 processor? Oh, that's going to cost you.

Even if you know how to make transistors, the actual physical plant required for a current microprocessor includes things like soft x-ray etching mask units with nanometer precision and ultra-fine air filtration units. Plus chemical industries to supply single-crystal silicon wafers. Plus the support industries needed (Sophisticated alloys from raw ores. The chemicals required for the photoresists. Process control sensors and electronics to control fabrication. Etc) None of these things are easy, and they are the end results of decades of incremental development. All of this from a colony which is just getting started and has no basic industrial infrastructure - and may well be investing a lot of effort to adapting agriculture to the existing ecologies/biochemistry just so they can avoid starving.

Depending on your FTL, it can get MUCH worse. I suggest you read Vernor Vinge's "Marooned in Real Time". He imagines space vehicles which are essentially made of assemblies (clouds) of nanoprocessors which modulate fields cooperatively to function. Presumably such processors are built by other, slightly less complex nanomachines. And they are built... Well, the regress in not infinite, but it's certainly inconvenient.

Interstellar Distances are just too large and they can't use high atomic number elements

I'm going to assume you want them to be able to venture into space at least to their other habitats but not much further than that.

Right now they may have access to asteroid mining where water is abundant. That gives them access to create hydrogen and oxygen propellant, which is what's used in modern chemical rockets. Hydrogen and Oxygen have smaller atomic numbers, so they're much easier to find out in space. Anything with a higher atomic number than iron needs to be created from a supernova. If they live in a region of space that has a lot of small stars, there aren't going to be many supernovae, so there's going to be very little of any high-density elements. Any high atomic number element like Gold could be used as the fuel, which is rare in space.

If they live around an average star, the nearest star to them is going to be 3-10 light years away. If we take the fastest speed any spacecraft built by people and assume that their spacecraft can exit their system with this much speed (which probably isn't true), it would take them 4060 years to reach a star the distance to Proxima Centauri, the nearest star to Earth. It's just not viable to send a rocket to another system because of the wait calculation. The wait calculation is question of whether we should send a craft to space now or wait later. If we send the spacecraft too soon, a new technology will reach before that spacecraft gets there. If we send it too late, we lose time to be at our destination planet.

It seems like your civilization has endured some losses in many respects including their home planet, why not technology? They may have some experienced people but not enough to create an interstellar drive. Consider what O.M said,

"You are obviously able to use a computer, like billions of people worldwide. And there are many millions who can program a simple website. But how many can design a microchip, or manufacture one?"

Gaining the technology to achieve interstellar travel from local travel is like technology jump from going to a bronze sword to an AK-47 or from an AK-47 to a guided missile. What makes this even harder is that advanced technology almost always requires access to new and unique materials. Why should an interstellar drive be any different? Just make stringent technology requirements on high atomic element materials, and your civilization will have a hard time acquiring it.

None of these obstacles make interstellar travel impossible, but it should take your civilization a couple hundred years (very rough estimate) to develop interstellar travel at the soonest.

For some reason FTL engines are attracted to what ever elements are used to fuel them, this is why the space ship crashed on the planet. The crash ruptured the containment field of the FTL engine thus causing all of the fuel element in the planet to be used up instantaneously destroying the planet, or possibly accelerating the planet to FTL speeds and sending it backwards in time allowing the inhabitants the time to discover the knowledge required to stop the ship from crashing on the planet. Aren't paradoxes fun. :-)

Idea:
The civilization is comprised of hundreds of small autonomous vessels (transportation, reparation supply) and a very HUGE one who can provide FTL capabilities for all the others (can create a wormhole?). The big one was totally anhiliated on arrival, and there are not enough material available / shipyard capabilites to recreate something similar.

The vessels are more or less self-autonomous and can be used to travel within the star system, but are unable to leave it.

There's nowhere to go

This is the simplest. They got stranded by a factor they cannot avoid and don't know previously. That factor can still keep they from reaching any planned destination. They are like a boat without a compass and with limited food.

Another good point is: They just cannot find another more suitable place to live. If you got a starship you do want a destination to arrive at, without destination there's no reason to get aboard that starship (or any ship).

While they might possess (or are able to recreate) the whatchamacallits and doohickeys that comprise the FTL drive they may have lost some

unique knowledge

of how they work together.

For example I'm writing a story where I needed to take the engines offline in such a way that they could be brought back online only after an extended period of time. In my scenario the engine field controllers were destroyed. The system AI can emulate the controllers but to do so it has to reformulate the resonance equations that were embedded in the lost controllers. Essentially an entire field of physics has to be rediscovered.

In your scenario you could make this knowledge prohibitively unattainable (until they discover it elsewhere).

Maybe they could construct a new FTL ship, but there's a reason their old ship destroyed the planet. It's an intrinsic problem of the drive principle, and they really do not want to destroy yet another nice planet...

Other answers cover how you can explain why they can't leave under their own power, but your question doesn't specify why no one else from home would send more supplies or a rescue vessel to eventually rescue them.

A very simple explanation is good old incompetence. This premise reminded me of the planet Wayland from the Star Wars Legends stories. The description of the planet from the game Star Wars: Empire at War sums it up nicely.

A simple clerical error in the Old Republic planetary registry removed Wayland from all known charts and doomed the expeditionary vessel seeking to settle a colony there. Without support from the Republic, the human colonists regressed technologically, discarding their blasters for bows and arrows, their modern fabrics for furs and hides. The colonists continue to clash with the two native intelligent species on Wayland, despite being forgotten by the galaxy at large.

So basically, someone at home accidentally hit delete somewhere they shouldn't have. Maybe they deleted all records of your system, maybe only the coordinates of the destination. Then they realized that backups hadn't been running for a couple months and it was lost. Or maybe it was simpler, someone had to manually transcribe the coordinates into their navigation computer and typed a "1" instead of a "2". A small change in a trajectory spanning light years will be many light years off at the destination, so all attempts to send supplies to the colonists ended up in the wrong place. The possibilities are endless depending on the specifics. Combine it with another explanation about being out of fuel or having a damaged part and you have your setup for how they were stranded and why no one is coming to help them. Many other answers here already cover that well.

The story is that the residents of Easter Island cut down their forest and couldn't build new ships (rafts or canoes). So they were stuck fighting each other for a fixed capacity of food production as population increased.

Their FTL technology warps them through space in a manner that was safe until a virus broke out that makes it fatal for anyone to pass through warped space. Later in the story the the virus is revealed to have been genetically engineered by [SPOILER].