You need 12V to run the refrigerator control panel, lighting, and the water pump. That 12V has to come from either the converter,(which can happen continually on shore power, without the battery working) or from the battery, when you do not have shore power available.
So if those items are functional, your converter is putting out 12V.
Your battery may be dead for many reasons---boiling off water (not likely if it is a sealed battery), old age, over-discharging, etc. Or it may simply have a loose connection, that is preventing it from supplying 12V or getting charged from the converter.
Verify that the battery is indeed dead, and if so, start looking for the cause. Correct any likely suspects such as loose/corroded connections, then get a new battery. Verify that it is charging correctly from the converter, so you don't kill off another battery.
You will need another battery to tow home. The battery is necessary to activate the brakes in case of a breakaway trailer while towing. If the trailer comes loose from the tow vehicle, there is a pin that pulls out, and that allows power from the battery to go to the brakes and apply them to stop the trailer. That mechanism is required by law for trailers over a certain size (which varies) in most states.
Single empty-nester in Middle TN, sometimes with a friend or grandchild on board
