How many of us have been burned by that comment? :)
Pick up a volt/ohm meter (if you don't have one) and check for yourself. Keith has a very good point. I've had batteries that show 12.5 but as soon as you start cranking they drop to 10 or below... the clicking and the lights going really dim points to a weak battery... but if that doesn't work, you might want to look for what took out the regulator, or what else did the bad regulator take out? The volt/ohm meter will be able to help with testing all of the little electrics along the way.