First, just to get things straight, it's not really a rinse tank. The tank is only for
soap and wax, and that water shouldn't get used on the rinse function. Forget that it says "RINSE" on it, it's hot water. Rinse is supplied by city pressure.
"Bay #5 no
soap" - does that mean water only, or nothing at all? Water only could be a solenoid problem, nothing at all would be the check valve. See if it has wax - if not, there may be a smaller check valve that's stuck closed.
Your bay 4 definitely has a bad check valve. Since rinse is fed at city pressure, it needs a check valve to keep the cold water from backing up into the hot water vat.
Any plumber should be able to change out your storage tank.