1995 Dodge Neon Engine start at times

Trying to help my friend son. Car start sometimes run for a min or two then stop will not start back untill when you turn the ignition key on and the battery indecator light fllash on then it will start then stop like discribe above. This is what I have checked, I have tried to scan with snap on scanner not comunicating with pcm. Check eng groud on or around trans. I only notice ground from bat to eng block. I am not sure if there should not be a ground wire to bell housing bolt or some place on trans. I notice it has a used trans. Second thing I notice the starter relay is missing and a wire has been run from bat to a added starter switch (push type mounted inside under steering columb) then wire from new switch to the connector where relay has been removed for starter. Thirdly it had some kind of sterio system that needed the direct wire from bat which was taken out and a added alarm system which was also removed. I have checked for power from ign switch to starter relay with switch in start position and there is none. I am trying to give as imfo as posible. The kid just both the car.