Battery charged but RV won't run on house batteries

unless you have an inverter (properly wired) the batteries won't run ANY 120V appliances, like the GFI outlets. All the batteries power are the 12V lights (likely all the lights), fridge on gas, furnace, WH on gas, etc. No microwave, No AC, maybe no TV etc.

Do the battery(s) have a disconnect that is turned off? Many trailers have a 12V disconnect switch to keep the batteries from discharging from loads like the propane/smoke detectors, radio on standby etc.