This use to happen to me when I had the 91LS. I Moved out of town to a new job for a couple of years and left the car with my uncle. He decides to put an aftermarket alarm on the car. I moved back after 5 years and got the car back, sometimes I would park but when I went to start the car nothing would happen. I could never figure out what the problem was since it would start after letting it just sit for 30-60 minutes. This happened several times before I found the alarm and ripped it out. I never had that problem again.