A healthy, fully charged battery should actually read about 12.6 - even a tad higher, depending on age. 12.12 is way low... Way low. And, if the charger is on/operational, you should either read resting battery voltage or higher (charging voltage).
I think the next step, before you do anything else, is to check the health of your charger (and the boat's charging system, for good measure). It's quite possible that a bad charger could kill a battery. There are tests that can be done to check. I've done them, but don't recall the exact procedure. I believe they are listed in the charger's manual, but you can also call PM and talk to them directly - their customer service is very good.
So, since it seems like there's a couple variables going on here, step back and check each individual component. That 12.12V battery may be kaput, as well - but see if it takes a charge (check fluid, if relevant)... for now, use something else besides your PM
When you get around to actually getting new batteries, you may want to consider a "dual purpose" battery. Generally, I'd like to have (2) dedicated starting batteries and a dedicated house system. But I've recently learned that Deka (who has always made a great battery) has a new(ish) dual purpose battery that would fit your needs perfectly. FYI, I learned of that battery through this site and am including the info posted by Doc Stressor:
FROM MEMBER "DOC STRESSOR":
The Deka 27m6 is indeed a dual purpose battery that was developed to meet the Yamaha requirement for a starting battery with a reserve capacity of 182 minutes yet also provide >800 cold cranking amps.
http://www.eastpennmanufacturing.co...ine-master-27m6-startingdual-purpose-battery/
It actually has more reserve capacity than their DP27 that only provides 650 CCA and a 150 min reserve capacity (minutes @ 25 amp).
http://www.eastpennmanufacturing.com/wp-content/uploads/Marine-Master-Spec-Sheet-0194.pdf
The point is that the 27m6 is the one you want in most cases.
I don't know if Gradys come from the factory with batteries, but all the new ones I've seen had 27m6s in them.