2001 Pontiac Grand Am What The HECK?

Electrical problem
2001 Pontiac Grand Am 4 cyl 117700 miles

Ok. I have a 2001 Pontiac grandam with a 2.4 engine. Today it randomly decided to pull this crap. I went out to my car to start it and when I first got in and put the key in the ignition, everything came on as normal(the radio, the lights inside around the speedometer) but when I turned to turn it over, it died. As if all the electricty had been drained. I turned it all the way back and took the key out and let it sit. I then tried it agian once or twice and still nothing. It wouldnt make any attempt to fire up, no noise or anything. After about three minutes, I tried it and it fired right up. The only thing that was out of place was the radio(stock) just said the time(which reset) and "Error". Me, figuring that somehow the battery had died and randomly found just enough to get it runnin, I let it run for about 10 minutes and turned it off. And it decided to do the shut down trick agian. It did the same thing on and off agian for the next few hours, just like it had done before. Then, as I went to leae work, it shut down, but when it came on, the radio started working agian, and the trunk popped up. So I drove down the road to an autozone to get my alternator and battery checked and was told the machine was broken. So when I went to leave, the brake warning light, the ABS light and the "trac-off" light came on. Started it up agian, and it went away. Drove it the 10 miles home to where it sits now. I could swear by the altinator being bad, but it doesnt make sence. If the altinator wasnt charging or the batt was dead, wouldnt it have to be jumped before it could run? Ive had some electrical problem ive never really had checked before. I was told I have a bad relay sensor in the dash(behind the radio I presume, sometimes makes a turn-signal type noise when driving, but not always). I was told it wasnt too big of a deal and not to worry about it. I did read it could be the car's passlock system and that it can be fixed by diconnecting the yellow wire that goes to the ignition switch. NAy ideas on what this could be and what I can do about it? I appreciate your time and help in the matter.