Batteries? You have two house batteries or both house & chassis battery? In either case a hot battery is not a good sign.
That isn't a "Shore" switch its a "Store" switch: Put it on Use whenever you are using the camper and put it on "Store" when its in storage and not being used (in "Store" mode it disconnects the coach battery from a bunch of stuff--but not all
). You leave it in Use mode even when plugged in or using the genny to charge up the house battery.
If you can't start the genny or do anything when its in "Use" mode with no 120v plugged in externally either you have a wiring problem or dead batteries.