Did you check the GLASS fuse on the board? That is the 120 element fuse.
It is 5 amp. I have never seen the E3 code but the manual states cooling unit problem which is a catch all for any problem causing lack of cooling. There is nothing on a Dometic that could tell you, you have a bad cooling unit. Doug
PS did you try this?
To preform a diagnostics test:
1) Turn off the refrigerator with the ON/OFF button.
2) Press and hold the TEMP.SET button, then press the ON/OFF button.
3) Release the TEMP.SET button. Each subsequent press or the TEMP.SET button will toggle through the list of functions in the table below: