its not the charge solenoid
when on shore power or generator power
its the "converter" that charges the batteries
possibilities are
blow fuses
loose connections
something like the storage disconnect switch is on
or the converter has failed
or the circuit breakerr in the 120v panel is tripped
you need to get a multi meter and start checking voltages
I assume your lights etc work, but run the battery down
meaning the disconnect switch is not the problem
since batteries charge from alternator and house systems then work for a little while, connections should be good,,which leads us back to a converter problem