battery dead, lights flicker, car won't start

I have a 1996 Pontiac grand am automatic with 100,00 plus miles. The dash lights and headlights began to flicker, the car's idle decreased, then stalled. I tried to start it, nothing. I jumped the vehicle, after about 25 minutes of trying to jump, it finally started, again the dash lights flicker and headlights flickered, dimmed and finally went out. The car again stalled. I replaced the alternator, jumped the battery again (30 minutes to take), again the dash lights, headlights flickered, dimmed and went out. A year ago I had a problem with shifting out of Park. An electrical switch was replaced and it has worked fine the past 8 months. Any help is greatly appreciated.