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.