Some basics to get you over a major hump in the learning curve may help.
When you mention the temp/pressure relief valve, it is not likely to have any connection to the heating process as it is there just as a way to avoid true emergencies. Things like the tank blowing up!
When the controls for bad, the heater can get too hot and too much steam and that is when the relief valve will let the pressure off by opening the valve! It relieves this pressure when the temp or the pressure go too high. But it does nothing to control the heating, just relieves any emergency situation!
We can sometimes get the wrong idea when we change an item and the heater starts behaving. what may have happened is while changing the valve, the wiring on the heater may have been moved around and made good contact again!
But that brings up where I see many try to do things without good information. There are different brands and different models of water heaters and I certainly do not try to keep track of what each one does nor how it is different from the last one I looked at to repair!
I recommend first looking at the outside of the heater for a label to get the brand and model number!
With that base, then go online and find a service and repair manual for that specific heater. You know it is Dometic, so then you need to get the manual that has the features you have on YOUR heater, not what others have on their heater!
If you like, we can help in the search and using the info but first we need to know which heater! No point in getting into all kinds of confusion when we can cut straight to the correct path with the right info?
Right now, as a general idea, the electrical heating will need 110AC coming to the heater controls, likely a board and a few simple parts, then to a heating element. That element will be a rod sticking into the tank. Kind of like what you might use to heat a fish tank only metal, etc.?
The reason for needing the manual is that it will give pictures of where to find the connections to check things like where that 110AC connects.
It may be as simple as a breaker has tripped and the power is not getting to the heater!
But that is where you need to know where to check!
Maybe check for any tripped breakers on the 110AC power as an easy starter?
Or it could be as bad as the board has gone bad, but that is why the manual is a good idea to avoid spending lots of time and money on changing things that are not the problem!
Willing to help on the search but we need the model number??