Strange problem

Hi, I'm posting because I have a fairly unique problem, and I'm not quite sure where to start looking. I drive a 93 Nissan Sentra SE, here is the symptoms: When the engine idles, the battery light slowly turns on, and the longer I drive it, the brighter it gets when it idles, When I'm accelerating and stop pressing the gas I hear a loud buzzing noise coming from around the fuse box area or behind the steering wheel. While it is buzzing both the battery light and the break light (next to my speedometer) turn bright red at the same time. Every once in a while when I try to start it, the battery is dead, and other times if I'm stopped at too many lights, the engine will slow down and eventually stop, and I need a jump. I don't know much about cars, but my father does.. he looked at it and is pretty sure it's not the alternator. Has anybody ever heard of anything like this or know where I should start looking for problems? Thanks in advance.

Sounds like you might have a bad ground on that fuse box or a shorted wire.