there is some confusion here
what make model inverter ?
does it have an internal built in "transfer swtich" and passthru for AC from shore/generator
do your 12 lights , water pump work ? when ? with or with out shore power
does the TV require you to change outlets to run from inverter, that is a possibility, unless the inverter has pass thru
they may not even be plugged into the inverter
a stand alone inverter with out pass thru DOES NOT work from any external 120vac
you say the control panel light is only on when shore power is on or generator is on,
could be a combo unit that is charging the batteries and has pass thru power, but the inverter function is dead
or the internal switch is stuck,
