1988 Mercury Grand Marquis

Hi, my marquis has been turning off on me for the last couple of days. When it first happened I had just drove it for about in hour in traffic with the ac on, it was driving fine. I go park it and come out a few minutes later and it wouldn't start for nothing. It sounded like it was cranking just not turning on. I then go inside and about half an hour later my stepfather comes by to look at it and it started right up. It drove without a problem. Same thing happens later that night. Turned it off and wouldn't start. So I left it and came back the next day it started, but later on that day it turned off on me while sitting at a red light. I had it pushed off to the side, a friend came and looked at it, he ran a few test, looked at my oil blah blah, but still wouldn't start, as soon as I was about to leave it I decided to give it one last chance and it started. What could be causing it to do this? The car is old but it only has 50k miles on it and was well taken care of. The person I brought it from had it sitting for awhile so could that have caused problems?