When you say you have shore power, do you mean that the
12V lights all work when you are hooked up and when you unplug they don't? If you have
12V lights when hooked up and don't have when you unplug then the
12V power is coming only from the converter. Even thought the battery is new, unhook it and check it. Also, you said , "batteries", are the connections between the two batteries correct? I have had new batteries go bad as soon as I got them home.
Good Luck. We are headed to Arkansas in a few weeks for a fall camping trip.