OK....did you press the button on the control panel located above the entry door? Basing this question on my 2012 Bay Star, and at one point in time, I also didn't have the inverter on until I discovered the little button on the control panel solved the problem.
Shore power does not need to be on for the inverter to work and the indicator light to be on.
Retired but busier than ever!
2012 Newmar Bay Star 3302
5 Star Tune, SumoSprings, Roadmaster Steering Stabilizer, Blue Ox Avail
Brake Buddy, 2015 Chevy Malibu