Hi nostrokin,
Congratulations on the new Trail Runner and welcome to the Heartland Owners Forum.
You may have a very easy to resolve problem. Normally when you unplug from shore power, the lights and other 12V DC gear will run off battery power. The fact that everything works ok on shore power and immediately fails when shore power is removed, demonstrates that either the battery is dead, or power from the battery has been interrupted.
There is a 12V DC mini-circuit breaker in between the battery and the Power Converter and Fuse Box. If that breaker trips, you'll have exactly the symptom you describe. The mini-circuit breaker is usually mounted on a buss bar located near the battery. You need to locate the breaker (it'll have 2 heavy red wires attached to the 2 terminals). There's a teeny-tiny reset button on the bottom. Sometimes it's easier to feel the reset button than to see it.
I've attached some pictures to help you locate it.
Also, you might take a look at our owner-written
12V Block Diagram and Diagnostic Guide. It has a full explanation along with drawings and a diagnostic flow chart.