first, it always helps to post year, make and model of RV that you have.
second, was the battery recently removed or have you had it checked? do you have a battery disconnect switch installed?
third, you have a CONVERTER, not an inverter, that charges the battery when you're plugged into shore power. an inverter converts 12v DC battery power to 110v AC power, to run things like tv's and dvd players.
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC