Heres the thing; I recently resurrected my old Subarru Brumby, been parked in a paddock for a year and a half. Got a massive battery into it, and it started like a dream (well, as close to a dream as an ancient car can). Got it up to the garage, cleaned out all the mouse-and-rat crap, took the seats out to clean, and left it idling peacefully, and it sounded almost better than it used to. Two weeks later, my brother looks at the battery, and it looks like it almost caught on fire! Nothing on, no radio, no fans, and i checked the engine and battery before i let it stand, because i wanted to know if there were any mice left. Checked the cab and no real evidence of vermin, the real question I've got is why would a battery (big truck battery) start to melt in a Brumby that had no power going through it? Could vermin do that?
I don't know about truck batteries, if its a battery that carries more overall power, then maybe you had a St. Elmo's fire type effect going on between the terminals via the body of the car for long enough to heat it up enough to do that??? Obviously I really have no clue and am pulling at strings though. I think it goes without saying that you should remove that battery if you haven't already... very though carefully lest it leaks on you. The plastic might be brittle now as well.
Any way you slice it, it sounds like there was a short that was pretty significant and a dangerous one. Maybe there's just simply now a new dead mouse in the undercarriage that you don't know about.
Electrical problems are really frustrating. I don't envy you at all.