Rayburn - great there was some confusion on here which one you was connected to. You are plugged straight into the four prong 50AMP plug i.e. not using an adapter and plugged into the 30AMP connector.
If you was plugged into the 30AMP side then that would answer some of your 120VAC problems.
You mentioned the converter awhile ago.. The converter run from 120VAC and produces 12VDC which replaces the battery when you are connected to shore power. It also charges your battery when you are on shore power. Should not have anything to do with being week and affecting your 120VAC issues.
If the converter AND the battery was not working or connected to the 12VDC side of the Power Distribution Panel it could kill your air conditioner thermostat which is operated from 12VDC. I dont have a 50AMP power distribution flow diagram here but this is a 30AMP electrical layout - maybe this help understand what is connected to what...

Roy Ken