Problem fixed. Apprarently it was a battery cable issue. Before attempting to restring the entire cable, I bought new terminal connectors, cut off the old ones, stripped the cable back far enough to find good wire, and attached the new connectors. Voila.

Fortunately, I had just enough slack in the cables to attach the new connectors and still reach the battery. But, if I have to do this again, I'll have to either replace them entirely or splice in an extension. Still cannot explain the short circuit sound I was getting inside the dash after shutting everything down. That's a mystery I guess I'll have to leave for another time.

Last, thanks everyone for the helpful comments. It's nice to have someone to brainstorm with.