Replace GFI, not many dollars and many times cure the problem. If two outlets are working the inverter must be on and that will show lower battery charge status. Two really check the batteries for condition a load test. For charge, put a light load on for a short time period, this sheds a higher than normal surface charge. Turn batteries off, let rest for a while then check voltage for charge. About 12.6 is full, 12.0 is dead and any thing below 12.1 is below 50% charge and you are damaging the DEEP CYCLE BATTERY. Not yelling emphasizing deep cycle, marine batteries have some deep cycle qualities but are not true deep cycle.
2004 Clss C 31' Winnebgo