Look for a small black plastic thing with a push button next to the house battery, push the button, see if 12 volt power comes on and interior lights etc. work with shore power disconnected. The separate aux/house battery disconnect switch in the control panel, operates a relay, it should snap when you operate the disconnect switch. If it is in on position, and the relay is working, you should have 12 volt power for interior lights, furnace blower, etc.
If everything works with shore power connected, the converter/charger must be working.