Ok you have two or 4 devices to check
ONE: Battery disconnect switch (Salesman switch) IF this is off the INVERTER will still likely draw power but...... The alternator, and the converter (if seperate from the inverter) can not charge.
If on shore power the inverter CAN charge but with the switch off it's the only thing that has power.. And that folks is my #1 with a bullet suspect. The salesman switch.
#2 is the isolator IF house lights come on once engine starts the isolator is good and the Salesman switch is lifted even higher
#2 now becomes a circuit breaker or the master fuse (Reverse polarity) Described in a prior post
But I'd check that salesman switch
IF it is a 3-position spring loaded marked USE/STORE push USe and listen for a CLUNK. No Clunk ask and I'll take you to the next step
IT can also be labeld "AUX" and may be either a 3-position (CLunks) or a toggle (may or may not clunk) But that's my guess. Salesman switch OFF.
Oh where is it. Can be on Dash or on a control panel somewhere. But often is on the wall in the step well where you can reach it standing on the ground.