Agh...trouble

Alright, I just got done installing my radio system, and have a wee bit of trouble.  I drive a 92 Accord EX Sedan.  First off, I'm running my front speakers off of my Alpine 7893 amplifier (which in and of itself has another problem), my rear speakers in parallel, and my 12" JBL sub in bridged mode off of a Profile California 640sx ( http://www.profileusa.com/calamps.htm#spec2)  I also have a Neo Mp3 player hooked up and a CB radio.  I just got a new battery on Friday and am already having trouble.  This morning, after waking up, I tried to start my car, but had no luck.  After school, I came home, adjusted the cables on the battery, and had no problems. I went to work, and after my 3 hour work day, tried to start my car, with again no luck.  I have made sure that the Amplifier goes off when the radio goes off.  Do I need a bigger Alternator?  If so, any suggestions?  I'm going to Autozone right now to see what help they can offer, but any help from you guys would be greatly appreciated.

Another thing that helps: My lights are acting funny.  When I went to get out of the car, my power was out (no power locks), yet, when I opened the car door, the lights went on.  I then went inside, and came back out to look at it.  When I opened the door, only the light on that door went on, instead of the dome light and about 4 others.