Have you checked the transfer switch right next to the inverter, above the propane tank? If you get power with shore and generator, that may be the problem. Unlikely but it might be the problem.
*UPDATE
Thanks for all the support. All the advice sent me in the right direction.
The problem.....the plug from a small black box next to the inverter was not plugged into the inverter, which was located behind a panel above the propane tank. I have to believe it was never plugged in at any time. the prongs of the plug still had the plastic boot that covers the prongs still on it.
Problem solved ! thanks to all !
Mr. Otters, that small black box is the transfer switch for the inverter. It switches power from shore/generator or inverter going to the refrigerator.
You're a good detective.