Changing heating Element

You didnt indicate whether the switch was defective or not. From looking at the image, it appears that the identified conductor (white) was cut. Have you tried to reconnect the wire (white to white) and see if the heater is working?
You can buy replacement parts from here:
https://pantherrvproducts.com/search.php?search_query=Atwood%20water%20heater%20switch%20§ion=product

I'm thinking when you say black box, that you also have a wall switch with a symbol like a lightning bolt and you switch that on as well as checked breaker panel to make sure breaker is on as well.
With that said, you'll have 2 of 3/8" nuts holding that black cover on. Remove top one and loosen bottom one and pull cover off. ( Be sure power is off to unit while doing this.) You'll find the element in behind it. Put a voltmeter on black to element (red probe or alligator clip) and (black probe) to ground where you see green wire connected to tank. Turn breaker on then switch at wall. You should hear a relay click and 120 Volts should show at black wire ( red probe) . If you've got 120 volts there, shut off all power, drain water heater and replace element.

Here is website for brochure and support center. http://www.atwoodmobile.com/water-heaters/atwood-water-heaters-brochure.asp

If it's electric it sounds like the elements.

Try this link and open PDF file and print wiring diagram. (page 7)

http://www.atwoodmobile.com/manuals/waterheaters/MPD%2093050%20PS%204.9.09.pdf

There should be access from inside RV to get to the back of water heater. Make sure you have the hydro breaker shut off. On the back there is a cover where hydro wires etc, go in to. That cover has to be removed to give you access to element. Once cover is off, you should see element down low. You may want to test for voltage at element, then check switch ( on side or top of cover) and reset at ECO, (push in on little reset in center of ECO ) just in case one of them was the problem, and save changing the element.Then carefully test for voltage at element terminals. If voltage there and not getting hot replace element.

Does yours have the little cut-out diode looking thing in the plastic jacket installed between power wire and thermostat? If yes, remove it from the circuit and connect female spade of wire, to male spade of thermostat,(just removing it to by-pass it) and try it now. Let me know what happens.

Yes. If your using it in an RV, your converter can supply the needed 12 volts, if it's not already there.

If you've checked at pressure relief valve ( careful, not to burn yourself just in case it is hot) by pulling lever and catching some water that comes out in a cup or whatever. If it feels hot out of there, check that by-pass isn't faulty. Not uncommon for valves to seize, and only partially open, or close, and end up mixing hot with cold.