My guess would have to go to the fuel accumulator. It's more or less a check valve to keep pressure in the system for warm starts. It's located inside the frame up in the center of the car just underneath where the ashtray is on the inside. My car did this a couple of years ago. It would start just after running. And it would start after sitting for about an hour or more. But it would not start after sitting for 20-40 minutes. I replaced the accumulator and it's been fine ever since. Many of these are going bad after 20 years in the cars. Your problem COULD be that the fuel pump is getting hot and not running until it cools back down, if you're sure that it isn't running when trying to start the car. Keep in mind that it normally only runs for about 3 seconds when the key is turned on then doesn't run again. Just my $.02. Mark N VIN 6820