Car wont start

I have a 1988 Pontiac Grand Am with approximately 171 000 miles on it. I bought the car a few weeks ago for 300 dollars. When I bought the car I had no problems with it other than the radio not working, so I took it to the audio place to put a radio and system in it. The car worked fine for about three weeks, then it started to not crank when left over night. So I replaced the alternator. The car still would not crank, so I replaced the battery. After replacing the battery, everything was fine except for sometimes I would hear a squealing noise when I had my bass up on my system. After turning the bass down the squeal would go away. The car was fine for approximately 2 weeks. A few nights ago, I was lighting a cigarette with the cigarette lighter and my radio lost all power to it and my cigarette lighter stopped working. I am assuming this was a blown fuse. The next day, a friend of mine was working on the window and touched the seatbelt relay, and it was hot so they said that I needed to replace it and took it out. I then asked them about my stereo system being wired into my battery, and they said that was not the correct way of wiring a radio system, and unhooked it. Now a few days later, My car starts to cut off when I am driving, even without anything electrical running, and when I came out of work tonight, it wouldnt start at all. I had a co-worker of mine jump it off. (Which took forever), and as soon as I turned on my headlights, the car went dead automatically. Does this mean that my alternator is bad? Or is it my battery? Or both? And is the radio the cause of the problem? Or the cigarette lighter? Or the seatbelt relay? Maybe the fuse that I popped has something to do with the car not starting?

Please Help!