Here are some pics to go with what Dave and Gary are talking about. I would add one more test "before" you pull apart the heating element. You can test the element in place to see if it burnt open, or if one side of the corroded & burnt to earth ground.
This RM2652 is a little newer than yours (2004 mfg date) but it should be close to yours.
There was a recall on these fridges and yours was in the recall. If yours has had the recall done, you will see this sheet metal cover over the burner area with a wiring diagram on it and a thermal disk switch pop riveted to the side of the burner tube behind the cover.
With the sheet metal shield off, the 2 red wires are going to the thermal disk switch. If your does not have the disk switch or the sheet metal, then the recall was never done. This is a free safety recall and still active, any Dometic repair place/dealer can do it for you. Just call and schedule.
Here is the PC board and the fuse Dave is talking about. The 2 black leeds under it are the electric element.
To test the element, shut down the 120 VAC and the 12 VDC power. Pull the 2 black wire plugs off the PC board. Using your ohm meter, test across the 2 wires. If there is no continuity at all, (meter will be OL if digital or no ohms if an analog meter.(the needle will not move) then the element is burnt open and it's toast.
The next test, is to check "each" black wire if it has some level of ohms/continuity to earth ground. Put the ohm meter on one black lead wire and then touch the the other meter probe to the green ground wires on near the PC board.Do both wires. Both should be an open circuit and no ohms or level of continuity to earth ground. If one of the wires has a level of ohms to ground, then the element burnt through to ground and may have affected the PC board when it did and the element is still toast. Hopefully it would pop the fuse first, but you don't know yet at this point.
A correct working element should be around 44 ohms +/- an ohm or so. If the ohms are very far off of the 44, let's talk about it as the wrong wattage elements did end up in some fridges and created problems. Assuming your element is bad, when you get the new one, you can test it before installing.
This pic is before the recall is done, but it shows the element Gary was talking about.
The element slides down into a sleeve. There are no real screws to hold it in, it may be corroded in though. Twist and wiggle it to break it free. You slide/push the new in one all the way to the bottom. If there is no room to get it out, then you will need to unhook the fridge and slide it forward in the cabinet. I have changed the elements, but the fridge was out of the camper when I did for other reasons.
Hope this helps and let us know how you make out.