Breakers are probably not relevant - they are usually for the 120v (shore/genset power) system, not 12v and battery. Besides, you state everything works on shore & genset, so the converter is able to provide 12v power. Clearly the problem is that the batteries are not actively connected.
Since you measured 12.8v at the battery and believe the battery disconnect to be ON, the only explanation I can see is that the disconnect relay (aka solenoid) has failed in the open position. Follow the big wire from the house battery +12v terminal to the relay device and measure the voltage at the two large terminals (there will also be two smaller wire terminals. From battery side to any ground should show 12v. So should the other side. If the relay is closed, the voltage between the two terminals should be zero. If relay is open, it should read the same as the battery voltage. If the relay is open, that's why no battery power. Then the question is why is it open when the switch is on. Let us know the status and we can proceed from there.