Car just quits on 1992 Buick LeSabre

I will be driving along when my car quits. doesn't spit or sputter, just goes dead. After 15-30 minutes will start back up and go a little ways then die again. The second time it stalls it will start right back up and run fine after that. Doesn't do it everytime i drive it but is certainly an annoyance when it does happen. When it originally started doing this it wouldn't quit while driving but if i had drove it a ways and shut the car off to get gas or whatever and tried to start it right back up it wouldn't start until it had sat for 15-30 minutes...please help! When it won't start, it turns over fine. All the dash lights come on. its got power and the motor is turning over fast, just won't fire.

2 answers
This Buick has older On Board Diagnostics. Unfortunately it hard to guess at the cause of this problem without being able to do some basic preliminary first hand tests and of course getting the car in a failed state improves the chances of quickly fixing the problem. An engine needs three basic things to start, mechanical integrity (the engine's components must be in synchronization with each other and the engine must be able to develop compression), the engine must get fuel injected into the cylinders (fuel must be injected into the engine ( there is a computer that takes inputs from many sensors on the engine, interprets these signals and decides when and how much fuel to inject into each cylinder) finally the engine needs spark to ignite the fuel injected into the engine, (the spark is also controlled by the vehicle's computer deciding when the spark arrive at the spark plug). If the components in the engine are not in synchronization due to a broken or "slipped" timing belt or chain the engine will not develop adequate compression to start and run properly. If any engine sensor has failed (crank angle sensor, camshaft position sensor, intake manifold pressure senor/air flow meter, coolant temperature sensor) any of these will cause the engine to fail to start by causing a loss of spark or fuel delivery. All these components need electricity to function, a failed fuse, relay, open or shorted electrical circuit could cause the computer, fuel pump or ignition system not to function. Unfortunately there are too many things that could cause your engine not to start to be able to pin point anything to specifically look for. Check for fuel and spark first. A failing fuel pump can be intermittent like this on a Buick or a failing crank/cam sensor can do this as well.
WOW! This is still here 6 years later.
Check (have the shop check) the main computer that controls the ignition as well as the ignition / spark control module.
The main computer was replaced on my 1987 Olds Delta 88 when it would shut down without warning. That fixed it until it started missing and shutting down. The Olds dealer's service shop kept it on an analyzer and running until it happened again. They replaced a couple of ignition coils as well as the ignition control module. That part is under the ignition coils. After those repairs it did not stall again.