If you have any GFI plugs, test and reset them. Occasionally, manufacturers will use one GFI plug to protect a bunch of non-GFI outlets downstream because they are wired in series on the same circuit. The non-GFI outlets are cheaper. Your inverter may be tied in at a different spot in the circuit. In many units I've looked at, the inverter operates only the frig. Any operable lighting is 12V when you are not plugged in or have the genny going. Do you have a wiring diagram? You may be able to trace your wiring and locate the problem. Start with the last outlet with power. Turn off the AC, remove the outlet and look for loose wiring. If it's okay, go to the next one in line.