Car Starts And Dies Right Away. Also Have A Burnt Plastic Smell In Car.

Weird Problem  1997 oldsmobile cutless The engine light has been on and off for a few months now. I had is tested at a local parts store which  indicated an emissions vacuum leak,  possible the gas cap, canister Purge valve, canister vent valve or for that matter an engine leak.  Well I held off on purpose, since these parts stores have been wrong in the past.  I did notice when I would fill the tank up the light would go out until the tank became a third empty.   Anyway I have no idea if this all ties together.    Last night after a heavy rainstorm which included thunder and lightning my dome light went on by itself.  A neighbor told me,  so I went out and had to manually shut it off because there wasn't any doors open to activate it, which was strange. Never had that happen before.    The worse was the burnt plastic smell inside the car.  So I started the car, fearing the battery was dead, and it started and ran fine.  The next morning the smell was still present.  The car started with no problem only for it to shut down immediately.   Looked under the hood and didn’t fine anything abnormal looking.  Would anyone have any suggestion what I could check for.