I have an issue that I did not see in the search, My 92 Si 3dr, starts (after sitting / cooling down) and immediately dies. It will then start and die or run (takes a couple times) but after that it runs perfectly. When the car dies, all the lights (oil / amp / cel / etc) are not lit. It is like you turn off the key. Could it be a relay or something, it runs great the rest of the time so I think it must be a connection or something simple, I don't havea lot of experience working on Hondas yet.

 

Check you Dizzy cap, sounds just like what happened to me, just replaced the Dizzy cap and it works fine now

 

Any time you have the key on but the engine not running the oil and battery lights should stay on. You are losing power to everything, could be the key switch itself, a loose fuse or wire, bad connections at the battery, bad grounds on the engine, etc.

 

"Any time you have the key on but the engine not running the oil and battery lights should stay on"

Thats what I was thinking, I just thought before I started chasing an electical demon, I would see if someone else had the same problem before.