[CaptainPalapa]

My first thought is similar to an old issue I had. 3 of our 4 lithium batteries had gone bad, in that if you wiggled the posts with a voltmeter the voltage would disappear and reapper. We had the same symptoms as you. Plugged in, things work (mostly) fine. Unplugged, and relying only on the batteries, no dice.

I would say unplug, then test those batteries again. If they are reading poorly, my thought is that your batteries aren't holding a charge or your charger/converter isn't doing it's job right. When you're plugged in, you're getting conversion from AC to DC, and into the 12v system, but not necessarily into the batteries.