I missed a detail when I read through your description, you said yo have power at the battery when plugged in or engine running? No power when everything shut off/disconnected. Are you measuring with a meter if so drop off the negative cable and recheck. If you truly do not have any power at the batteries with the cable disconnected one or both batteries are bad. Further testing I assume you have 2 6 volt wired in series, + goes to - on the second battery and only 2 cables leave the battery compartment, one positive from first battery and one negative from the other battery.
