2002 Pontiac Grand Prix Battery issues

I recently had to replace my battery after about 5 years. I figured with all the cold weather we have been having and the age of the battery that it was just a simple issue. After installing the new battery, approx. 24 hours later I went to start my car and it was difficult to start, but when it finally did the battery light was on on the dash. After about 15 minutes or so it finally went off. The next couple of days it did the same thing. I had autozone test my battery and alternator and they said it was fine. My dad knows a bit about cars and did his own test, (take the negative cable off, the test you have mentioned on here), and said that it was not the alternator draining it back. We went through the car piece by piece to figure out what the problem was and it came out being the "stereo amp" (I did not even know there was an amp in there, but turns out there is a factory installed BOSE system). So I pulled the fuse on it and so far that has solved the battery dying problem. On the other hand, now my radio does not work. I am trying to figure out if the amp can be bypassed from the rest of the stereo until I can either replace it or get it repaired, without damaging anything, OR if this is something easier and more simple to fix, such as a fuse. The fuse that I took out was not broken internally but it was rather charred on the prongs. And also, previous to this happening, for most of last summer while driving and occasionally hitting a hole in the road, something would start whining and sounded like it was coming from the speakers. Everyone I talked to about that said it was a ground of some kind. As you can probably tell, I do not know a whole lot about cars, but am trying to learn. Although my dad knows more than I, he does not know how to fix this problem. I am really hoping you can help. Thank you.