New battery, no interior lights

As OG says, get a Meter and start checking. Personally, I'd start by disconnecting the battery, hooking up to shore power and testing the connection clamps. My bet is you will have voltage showing from the converter. 

If you can get the lights working from the Tow Vehicle and not the house battery, I suspect it's on the battery feed lines. There is a auto-breaker that comes off the battery under the trailer, exposed to the elements. Mine was right up front, just follow the wiring back off the battery. Check it on both source and feed sides.