92 olds eighty sometimes starts

i bought from the auction other day with 109K on it had power but no starter spin. went to it last night threw a starter on it and it started. got dam near home and it shut off. acted like it wanted to start on start fluid but didnt. i put gas in anyway,because i never seen the hand moving. still didnt start. i noticed when i cut off the ignition all the dash warning light would dim out slowly,never seen it before. i get these models all the time and the lights go out instantly.:banghead: however i pulled rest of the way home with my truck and put spark tester on coil and it sparked and fired right up. ran a couple minutes while i parked my truck. cut the olds off and i be dam! no start again just spinning but has good strong spark. anyone has any ideas on this one? i havent even begun to look yet but was seeing if anyone has any ideas or had a similar problem

1 - Check the battery cable connections. Remove the bolts and rubber boots so you can clean all the corrosion off the cable ends.

2 - Check for spark at each of the 3 front cylinders.

3 - Check the fuel pressure

4 - Check for fuel injector pulse.