Two things contradict:
With shore power on that means the converter (not inverter) should be on and that means you should get all the lights on the monitor even with no battery at all showing "full". Two or three out of four would indicated no converter on, just what the battery is doing.
But, turning off the breaker to the converter (bright lights if the converter is working) would put you on battery (dimmer lights) so converter must have been working
So either the converter works or it doesn't, which is it?
