I just replaced my radiator, thermostat, downpipe, uppipe, and battery, which was only putting out 1 amp. Upon turning on the car after this was all finished, I noticed I my dashboard lights were not on. The inside car lights (the ones above your head as you sit in the car were not on as well. Upon taking the car for a drive, I noticed that the ABS light goes off when I turn the AC to 3 or 4, and a clicking noise can be heard from the fuse box. My brake light is also comes on upon acceleration, but turns off during idle. I have looked at all the 10,15,20, and 30 amp fuses. I noticed that the 15 amp door lock fuse had busted. Once I replaced that, the dashboard lights came on, but everything else was the same as before. Also, when turning the AC onto full blast, the lights sometimes dim. Also, my keyless entry system makes a the beeping noise but the doors do not lock. Even when I manually lock them, they cam be opened regardless. When I push the lock on the door a little further than required to lock it I noticed a rumbling sound like the car is trying to lock the doors but its not catching. This happens on all of the doors. Any suggestions?

alternator? 2 separate problems?

I agree with Wrxguy27, there are two problems here. At first thought, I thought the alternator was causing the brake light to come on but it really may be due to low brake fluid level so check that out.

The other problem is most likely due to a bad chassis ground connection. I suggest you remove all the ground connections and clean them, especially the ones near the battery. Clean the battery connections also. If that doesn't help then there is a bad connection in the power buss somewhere to those areas that are having trouble. If that is case let us know and we can get some further details on where to look for the trouble.