Chevrolet: Anti Theft, chevrolet malibu, computer readout

Question
My 1997 Chevrolet Malibu has a problem of not starting for ten minutes or more.

Dealership has replaced, by second guessing problem, ignition switch and assorted other parts and computer readout shows no service code problems. Dealership says,"cannot duplicate problem".

I have contacted General Motors customer service and was told to take it back to dealership and try again. I think six wrong guesses in two years should be more than enough. I do feel for the dealership.  

Answer
When does it do this? Randomly? When the car has been driven for a bit? When the car is cold? When the car is hot?

What trouble lights come on when it does this? Do you see a security light?

Do you have a black computer chip in your key?

What sounds does the car make when it won't start? Does it make a clicking sound? Does it click once or rapid clicks? Can you hear the motor turning over? Or is it completely silent?