Duo Therm Heat Pump weirded out

Everything has continued to work OK, but I will repost when the relay fails again. I have a spare control box that I'll take with me. My friend who was in the Alpenlite when everything went south said the twelve volt power was basically gone with no twelve volt lights working (It turns out I had a bad battery that drew everything down and even caused the Xantrex inverter/charger to shut down on a low voltage safety). Then two twelve volt lights flickered and the thermostat display suddenly came on and the compressor started running. He realized that the fan wasn't running so he got up, and not knowing what all my breakers were, decided to shut off the main breakers. That of course shut everything down. Then that relay would not release. I started to say that only the compressor would run after that when 120v was supplied, which is true, but I just realized that with the built-in time delay, I probably never let it run long enough for the thermostat to cause the unit to turn back on and start up the fan. I was concerned about pressure build up without a condenser fan running. Anyway, that's the most complete description of the chain of events. My friend said that definitely a small surge of 12v power came back for a short period and that's when the relay stuck (although maybe the cause and effect could be reversed, since all we know is that the events were basically simultaneous). I had come over about an hour before the lights flickered and started the Xantrex back up, but the safety would only let run a few minutes at a time before shutting down. It would go into bulk charging at around 85 amps but then shut down after maybe a minute or so. I did it around five times until I figured there had to be some protection circuit, which I later verified was the case. I've surmised that I got enough charge during that time for the twelve volt system to momentarily come back to life and that's why the lights flickered and the thermostat display came back. I hope this makes sense.