Pardon me if I misunderstand. I'm reading the first post repeatedly and see no mention of house batteries. The house is not powered from the engine battery - rather from at least one battery in a compartment with ventilation accessible from the outside of the house. The first thing I would check is the voltage on the house batteries. If below 12 volts they are not charged, and if not charged for a long time they are probably ruined. Check the charging system by measuring the voltage on the batteries while hooked up to shore power so the converter should be applying at least 13.5 volts to the batteries (fuse for that may be somewhere other than the house fuse panel).
