Yes. Look around for a burned spot. 30 amps will definitely leave a mark if it shorted.
As for the 13.2 working on a very low battery not is not out of the question. That should come up after 8 to 10 hours. If at that time you unplug the shore power and the voltage drops below 12 I would say you have a shorted cell in the battery.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles