The house bank and start battery should be completely separate. But you've had not 1 but 2 coincidences. On your boat, the state of the house bank seems to influence the start circuit. Before I did anything (like take the boat somewhere), I would label and test the entire start circuit. Maybe a previous owner made a "modification".
It could also be 2 problems; you may have a problem in the ignition/starter circuit, the start stop solenoid, or something else.
Sounds like a long weekend with a multimeter.
Tom and Kirstin