1) With the power OFF - No shore power - Black Wire OFF battery.
2) Pop the switch plate off (sounds like you did that before).
3) Swap the entire wiring set with the switch next to it.
Feel free to put the removed wires from that switch to the suspected "bad" switch.
4) Check all wires are firmly connected.
5) Connect the Black Wire to the battery
6) Check for correct light operation using the outside light switch to operate the inside lights.
7) If all is ok now, then check the outside light using the now suspect switch. If "No Go" replace switch.
8) If outside light works fine, and the inside lights are still bad, you have a wire issue. (this is highly unlikely since the lights are working and power is switched on and off, not the ground).
Power would have to be bypassing the switch assembly to get to the lights. If the lights were not working AT ALL, then its possible you have a bad ground connection.