I had a similar problem when I ran my generator after an oil change while plugged into 30 amp shore power. After I shut the generator down, I had no refrigerator ac power. Also, there was no ac power to the inverter. I'm not sure what other ac functions were dead. Most of them were working. This is in a 1998 American Tradition which has a Heart Interface inverter which also handles the switching function between generator and shore power. What I found was a stuck relay that does the switching between generator and shore power. The relay apparently pulled in when I started the generator to switch over to generator power. When I shut down the generator, the contacts were "welded" together and did not release to allow the relay to switch over to shore power. I manually broke the contacts lose and all was well.
Look for the generator/shore power switching relay and see if it is stuck. If you find it, you can shut down the generator and be disconnected from shore power and use an insulated screw driver a non-conducting probe to manually engage the relay to see if it is stuck. If it is, you should be able to break it loose. If it was stuck, you might want to get a burnishing tool and clean the contacts. BE CAREFUL LOOKING AROUND THAT AREA, IT IS HIGH VOLTAGE (120 V).
Jerry