A few things going on here.
The "park" water inlet is where you'd connect a hose, connect it to a hose bib and pressurized water will feed the trailer without the need of the pump, or filling the tank. The fresh tank fill is a port you'd use to only fill the water tank, with a hose, bucket or jug.
Whether you're using city water or the storage tank & pump, the water heater will heat the water it it's tank.
So, the question now is whether you have pressurized water coming from the fixtures, whether it's city water or provided from the storage tank and water pump. It's implied you do, since you say the water heater isn't heating and you wouldn't know that without running water (just walking through the process here).
If this is an electric-only water heater, you would need to be plugged into shore power for the water heater to work at all. If it's a propane water heater, you need a source of propane and it needs to be turned on. Some water heaters have both electric elements and propane burners. Whatever the case you'll also need a source of 12V power for the heater controls.
So, questions:
What kind of heater - electric, propane or both?
When you run a hot water faucet or fixture, does any water come out?
Any appearance of heater control operation? (Lights, switches)
Does water come out of the overpressure valve (OVP)? CAUTION - COULD BE HOT
Purging air from the OVP is not "bad" other than the hot water burn hazard.
Mark B.
Albuquerque, NM