The battery does not need to be hooked up at all for any of the 12v DC appliances to work assuming that you have plugged the 120v shore power cord into an active outlet at home. I'm guessing here but by mentioning that your Jayco is a Designer series, it's somewhat recent. If you could provide specific year/model information, that would be helpful.
As part of the troubleshooting process, figure out what DOES work. Do the 120v AC outlets work? That tells you that the converter is at least partially working. Plug a household lamp, lights or radio into the outlets and verify.
Do any of the other 12v DC appliances work - i.e. does the water pump work, will the furnace kick on? Do you have a automobile style radio built into the PUP and does it work?
If so, then you've at least determined that the converter is not the primary culprit.
If all else works and you don't have interior lights, then focus on the circuit and electrical wiring that controls that. Jaycos usually have a micro contact switch on the road side of the PUP, towards the rear and just up under the roof line. When you raise the roof, the switch allows the circuit to be completed (or not shorted). If this switch is damaged, it could be preventing your lights.
It will look like this switch but only instead of having the arm with the wheel on top, it will be inverted with the arm and wheel on the bottom side. Again, this should be on the road side of the PUP up under the roof mounted on the side wall of the roof.
This may be the next culprit in line. But I would start with swapping out the fuses. That is the best, easiest place to start. Replace them all for peace of mind, if you want. But I would replace them with new fuses one at a time, so it will help you determine what is powered by what fuse and subsequent circuit. Not a bad time to make a label of what fuse controls what items inside the PUP. Jayco did OK but not great at labeling the circuits.
