Hello and thanks for your help so far. To give more info...
We do have a large, permanent inverter near the battery compartment, and a smaller, portable one that we plug into the dash receptacle so we have 2 outlets for devices that don't have cigarette plugs.
Husband bought 4 new batteries today. No change in status.
We had flickering lights when we used the water pump this weekend while boondocking.
When we switch from shore power to generator, the large inverter changes from a humming noise to a single click and then no noise.
Breaker switches located on large inverter turn various things on and off. Two switches that each control half of RV.
We have checked every breaker, fuse and switch we can find. Husband is continuing to go through every nook and cranny looking for one of the above.
The following are items that are working or not. There is no change with the generator vs. Shore power:
Cigarette lighter receptacle in dash NOT
House lights NOT
Both TVs WORKING
Microwave WORKING
Water heater NOT
Water pump NOT
Fridge (residential, only uses electric) WORKING
A/C no power to controls/thermostat to turn them on
Power outlets WORKING
Washer/dryer NOT
Cargo lights NOT
Thanks again. Keep the ideas coming!