GMC Repair: 1991 GMC SONOMA does not start, gmc sonoma, battery cables

Question
This truck starts with jumper unit. It has a fairly new battery. It does not start by itself. After started, it stops running if my foot is off the gas pedal. Its alternater and starter was rebuild recently by a shop in local.
Is this a problem with electoric, O2 sensor, fuel pump, fuel filter, or something else?
Please help me to pinpoint the problem so I can fix this without taking everything apart by myself.

Answer
Hi,Blade.

I would check the battery cables making sure they are clean and tight,but what it could be is a failed ground ckt/wire,check the ground cable that goes from the battey to the engine block,make sure its clean and tight,also there is a ground wire that is located on the back of the left cyl head,there is a stud with a locknut,make sure that is tight,ive seen these loose causing the same complaint your having,also in rare cases ive seen the battery shorted internal,have the battery checked making sure it isnt shorted internally,if you need more help contact me and ill see what i can do.Thanks

ED