Check the wiring coming from alternator if the ground is bad or weak you'll get similar results. This wiring harness is easily "chaffed" from vibration, etc. Check all the connectors - sometimes if they get hot the plastic will melt or connectors will corode or tarnish. Your regulator is in the alternator so I don't suspect that to be the problem. Some also have a fuseable link (looks like a large fuse) inline and your old alternator might have fried it. Get a small voltage tester (Radio shack, home depot - $10) and make sure you have 13+ volts at the battery when car is running.
