Let's see if I can find anything out here that will help. This will be a lot of information, maybe too much.
Ok.
About a year ago, someone tried to steal the battery from my car. They cut the wires, and when they realized they couldn't remove the battery, they left it alone. (I know that someone was trying to steal it because the same night, my roomate's battery was stolen, successfully). I rigged up a new terminal and re-attached the wires.
Later, the battery died. (It was old. So it seemed normal.) I replaced the battery, but after that the battery gauge sporadically dropped. It was fine for about a week, with the battery light coming on every once in a while, but it never affected how the car was running.
But then the power failed, and I couldn't get it started again. I had to have it towed to the shop, where the mechanic replaced the alternator. (I had had a feeling that the alternator was a problem for some time, so it seemed like a sensible solution). I drove the car for two days after that, and now it's died again. The battery light comes on, the lights dim, and then I can't accelerate. If I leave it alone for a little while, it starts again, but only runs for a short time.
If I assume that the alternator is fine (since I just had it replaced), what else could be the problem? Is it true that if the car starts, then the battery is probably ok?
I really don't have any idea what the problem could be. Bad connection from the battery? What?
Also, the Jeep just died in the projects, which is pretty awesome.
Any help or advice would be enormously appreciated.