Its very common for the manufacturers to combine the converter power and the fridge 120v together on a single breaker, so tripping off the "fridge breaker" also kills the converter. That is why the fan quits.
It certainly sounds like this is a battery issue however.
'03 Ram 2500 CTD, 5.9HO six speed std cab long bed Leer top and 2008 Bigfoot 25B21RB.. Previously, 2008 Thor Freedom Spirit 180, SOLD! 2007 Winnebago View 23H Motorhome, SOLD!