HS, sounds like you have a battery cut off switch, that has been tripped/turned off. Might be under the hood, trace the power cable's back from the battery's, and should locate it?
The outlet in the compartment is what TQ60 said, to plug the power cable into when the gen. is running for house power.
You say you have power when plugged into shore power, trace the power cable into your MH to find your converter, once you find it, check for a door on the back, inside you will find a couple of breakers, make sure they are not tripped!
As for the lights on the outside top, they are wired up in series, pull each light out, find the first one, then check to make sure you have power at it, if not, trace that wire back, till you find the problem.
Hope these things I have suggested help!