I feel like a major dummy. Right away I took the cables off and then put them back on, kind of twisting them figuring that would take care of any bad connection. They weren't gunked up with the white powder you get from a leaking battery. I was going to borrow another battery from my dad and he gave me his battery terminal cleaning brush too. I figured I'd try really cleaning the terminals on the battery that was in the car good first and that was it.

I have had another vehicle where the battery terminal connections got gunked up but on that one I tried to start it and it clicked once and then was totally electrically dead. On the Charger there was still some current passing, enough to make the mutimeter measure it but even the load of the dome light was enough to cause the voltage to drop a lot and there wasn't enough voltage to even engage the stater relay or solenoid.