Gary RV Roamer said:Your heater will have both a thermostat and an emergency cut off (ECO) to control the electric. Older Atwoods have a separate thermostat for the electric heater but newer ones share one thermostat for both modes. There is a seprate ECO for each. I'm confident that a 2004 is the shared thermostat type, which means there is a switching relay controlled by the heater's main circuit board. The relay switches 120vac power on/off when the board gets the "heat needed" signal from the shared thermostat. Note that you must have 12v power to the heater circuit board to enable the circuit board to activate 120vac heating. Make sure that you have 12v power and the circuit board is working before you decide the relay or ECO is bad.
As Alfa says, you need to identify the heater make and exact model to get the right parts. Many control parts are shared among several models, but not all of them.
I have never had a 12v battery hooked up to my camper. I was told I didn't need it. I have or had used the water heater with electric for over 2 years(summers) till it broke last summer.