Battery alternator power problems HELP!!

Hi all. Thanks in advance for help.

I have a 96 Cavalier LS 110,000 miles and a while back I started having weird electrical clicks. After I would start the car, I would get this click from under the dash, but can be heard from the engine also, and my radio would turn off, lights dim, etc... but the car would run just fine after that. I'd also had intermittent problems with the horn clicking when pressed and the wipers not going back down all the way. Few weeks ago car stopped running while driving and I shook the negative battery connection. It started right back up just fine (this happened 2 times in last 3 weeks). Well today, everything same. Went to leave work and it would not start. I got a jump, but as soon as I put the car in drive, it died again. I got a new battery and the car got me home, but I think I've got a bigger problem, such as a relay draining my power perhaps, or a bad alternator. Any ideas if these are all related, how to check relays and anything else? Thanks!!

Justin
Orlando, Fl

Test you alternater and check for a draw.