Hmmm, maybe there is some gas that is very slowly leaking somewhere but I am starting to lean towards checking the ECU. You have a first gen ECU which is known for having leaky caps in it. I had the same problem with my car. It would start up fine, drive for a bit, and then shut off and not want to turn back on after getting warmed up a bit. It is really quite simple to check if any of the capacitors have been leaking. Your ECU is located behind your radio. You will want to take off the carpeted panel on the side of your middle console. It consists of a couple screws and snaps. When you get that take off, you will see a bunch of wires running to a somewhat goldish metal box...that is your ECU. Disconnect the wires from the ecu and then unscrew the ECU from its mounted position. Once you have the ECU out you can unscrew a couple screws on the ecu so that you can take the top off of it. Once you have done that, check for any caps that could have leaked on to the board. If you see any that have leaked on to the board, that is your problem. Sometime they can be cleaned and saved but more times than not you will have to buy a used/rebuilt/new ECU. I went with a rebuilt ECU.
Here is a pictuer of the ECU being pulled out:
