Be Careful the hot water heater is full of most likely 140F water.
While this may not open the check valve, it will help confirm the check valve is the problem.
The winter bypass valve. the white valve in Gary’s pic, between red and blue hoses.
If you flip that valve to bypass, it will bypass the hot water heater. Water should flow from the hot water faucets, but will be cold.
If no water flows with bypass flipped then the problem is deeper. If it flows, then 1 of 2 check valves can be stuck
The brass one on top that you have been whacking on.....
Or the gray one (normally gray plastic) on the inlet to the HW heater.
I would guess the top one is stuck first but I have heard others have had the bottom one stick closed and then water cannot get into the heater to even get out. They check both the in and out direction for different reasons.
To see if the bottom one is stuck, turn off the incoming city water and or pump. Put bypass back to normal operation. Open faucets to bleed all pressure out of the system. Turn HW heater OFF, both gas and electric. Then if the water have cooled down in the HW heater, and you have a drain valve open it, be care full the water may still be hot. The upper brass relief valve can be used too but put a pipe or gutter over it or you will drench your electrics.
Once all pressure is gone inside the hot Water heater below the safety relief valve. Then with the relief valve open, slowly turn on the incoming water to the camper. New fresh water should flow into the heater and out the relief valve. If it does then you know the inlet check is open. If it does not and the bypass is closed, then the inlet check is stuck and cannot let any water in. If water goes in, comes out the relief valve and not come out the faucets, then the top outlet check is the issue.
A possible get it going fix once you know which valve is stuck….
If you let the HW heater cool down so when the drain is open outside cold all water comes out, then bleed all pressure out of the HW heater and all water, with pump turned off and incoming fresh. Then unscrew the plastic fitting to both check valves and push the check opens to maybe break it loose.
The bottom one free flows into the HW heater, the top one free flows out of the HW heater.
If you do not follow the intent of what I’m saying, don’t try this. 140F water can give bad burns.
PS if you open the pipes, make 100% sure all pressure is gone, faucets open and HW heater is drained. If not there are 6 galloons of water in the HW heater that can come inside the camper. = Not good...