Some info the O/P posted in his original post is important.. He said if he turns on the inverter power to all outlets.. This means any breakers on the inverter, if any, or in a sub panel, if any are functional and are SET not Tripped and thus we can eliminate those.
He said the batteries are NOT charging.. On this type of inverter this is often a function of a different module inside the same box
This inverter contains (usually) 4 main modules
The Inverter (Working)
The charger (Not working)
The transfer switch (Unknown)
and a control board (Unknown)
Here is how it functions: 120 volt power comes from the main breaker panel, usually a 30 amp breaker, (Could be a 20) to the inverter.. The control board senses this and tells the transfer switch to go to PASS THROUGH mode, it also reads the battery voltage and commands the charger module (This board controls ALL functions)
My guess is that 120 volts is not getting to the inverter.. Suspects include...
IF the rig is 50 amp the master automatic generator transfer switch (IF you have two air conditioners do they both work)
The breaker for the inverter
The connections on the wires to the inverter (PRIME SUSPECT) both ends
And finally the inverter's control board and transfer switches.
But my guess is a bad connection on the inverter's "Shore power" side (120 volt wires to the inverter) Check them First.