I see two possible problems both with the house batteries.
1: As discussed above, Bad batteries (wore out)
2: Bad (dirty) connections in need of cleaning.
Question: (before you ask) HOw do you know it's the house batteries?
ANSWER: The engine starts, it is much harder to start the engine than the generator so if it works when the engine is running, It has to be the house batteries.
Recommendation: PM the connections (Clean) and have the batteries load tested as described above.
What was I doing yesterday: PMing the connections of course.
