Sounds like when the house batteries are weak you cannot start the generator until you start the engine... correct? Sounds like your generator is started from the house batteries which the alternator on the engine is charging enough to then start the generator.
Do you have a switch by the door that disconnects your house batteries? While hooked up you have been running off your converter so I would check battery cable connections for loose or corroded including the negative cable at the frame.
None of the things not working have breakers, they have 12V fuses, but they are not getting 12V. You have a 12V problem which means the house batteries or cable connections or their disconnect switch turned off. Some 12V systems have a 150-200 amp fuse in the system, usually near the batteries.
