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1993 Oldsmobile Cutlass Ciera with 81,000 miles on it.  

Hi, I hope someone can give me some idea about what is wrong so I don't go blank-faced to a mechanic.... I can't find anything at all on the internet that fits this description.

Here is the problem.  Sometimes after turning off the engine, if I try to re-start it, it won't start until after it sits for a couple hours.  Once it has "rested", it starts right up with no difficulty at all.

It seems to be related to idling a lot, as in just sitting with the engine running, or stuck in traffic.  As long as the engine isn't turned off, the car keeps on running without a problem.  Things like lights, radio, etc still operate when the car is not starting, trying to jump start does not get the car going - the car just has to sit there.

When it doesn't start, initially there is no response at all, I turn the key and there's absolutely no noise.  As the car sits not on for a while, the engine will then acts as if it is trying to turn over but acts like the car would act if the battery was dying out (except, as stated, radio and all still work), and if I keep trying, it goes back to making no noise at all.  After sitting a while longer without trying to start the car, the car starts right up as if nothing was ever wrong.  

Any information you can give would be greatly appreciated.  Thanks!