1996 Ford Taurus Bat S- Crazy Electrical (?) Problems 96 Fo

My battery light came on the other day, so we replaced a cracked cable. That didn't do the trick. I drove it the next day and the light stayed on, and while driving, my stereo cut out, my tach went to 0 and after a short while later the airbag light came on, the blinkers started clicking without being touched, then the car died. We replaced the battery. It just happened again. I had to be towed home. Has anybody heard of this before? Is it my alternator? We had that checked, and they said it tested fine. Help!