I assume you've checked the power outlet you're plugged into. If it's OK, I think you're going to have to go to work with a multimeter and start tracing your power, starting with where your power cord connects to your transfer switch. If that's OK, check the output side of your transfer switch. If it's not OK, your cord or plug is bad. If it's OK, you'll need to check the wiring diagram for your rig at the following link and proceed to follow the circuitry until you go from power to no power:
https://winnebagoind.com/diagram/Wiring.htm
I'm a bit confused about your statement regarding no power at the coach battery switch. It should be 100% 12v and totally independent of your 110V AC power. As long as your batteries are good, it should work as should your 12V lighting.