Opnspaces, if he had 6v batteries wired in parallel, then the a/c and fridge never would have worked at that low voltage. Besides Group 24 is a 12v deep cycle/marine battery.
Sounds like the converter is not charging the batteries. The fridge and a/c need 12v to power their control boards even when they are running on 120v from the power pole. The polarity protection fuses on the converter are a pair of 30a (green) fuses that protect the converter/charge if you connect the battery backwards. Look where you see the automotive-type 12v fuses. If you post a pic of the converter we can point them out for you.
From what you say, it sounds to me like the converter/charger is shot. Progressive Dynamics makes converters that install in your existing power center...you don't have to replace the whole thing, just the converter/charger section. Progressive units also have a good charge profile that will go into 14.4v "boost" mode to give you a quick recharge when camping and also a good "float" mode that won't boil the water out of the batteries if left plugged in at home for long periods.
Get the make and model of your existing unit and look for a replacement on
Best Converter.
Note that units are sized based on DC power...so even though you plug in for 30 amps a/c power, the converters in trailers are usually either 45 or 60 amp models. The model # sticker on your unit will tell you.