Sounds like two separate problems. If you have 120V at the main breaker in the power panel but not at the other breakers I’d guess the main breaker is faulty, as unlikely as that sounds. Did you also check continuity on the neutral and ground from the panel to the shore plug? Just asking,
You said the generator won’t start. Does it turn over on the starter? I’m assuming not. There likely is a breaker near your house batteries. If you can find it look for a yellow or red “flag” that will reset the breaker when you push it back in.
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