What part is going bad
Starts right up, runs for 10-15 min then cuts off. Has to wait an hour before it
will turn over again. Starts right up again. It is not overheating, not the fuel
pump. Whole dash lights up just before it cuts out.
Engine computer might be going bad, knock sensor might be triggering, hard to say without more info. Check some simple stuff first, like battery cables and grounds. Your car does have a diagnostic port but it predates OBD, it requires an analog meter to read.
The part about the whole dash lighting up really throws me, I'm thinking maybe an over voltage problem or a check relay is kicking in when it shouldn't. This one you may just have to bite the bullet and take it to a shop you trust and have them check it out.