95 Pontiac Sunfire Electrical Problems?

I have a 95 Pontiac Sunfire 2.2, I was driving and my battery light came on so I went to autozone and they told me it was the alternator. I bought one and on the ride home my battery ran out of juice. I had my father bring me a battery just to make it home. I started up the car and my dash lights went nuts. Airbag, seat belt, ABS, Brake, and also a flashing headlight. I got it home thinking it was just because of the alternator but after I changed it the lights were still on. I noticed that when I turned on anything that would pull juice(A/C, Radio, headlights, wipers, etc.) all the lights would dim in the car, A/c would die down, radio cut out. Everything looses power. I took it back to auto-zone and said it was a bad alternator so I exchanged and same problem with this one. They tested it and it appeared to be good. I took it to my mechanic and he thought it was a switch for the lights but it wasn't. Can you help me out?