Pictures are worth a million words. Some comments.
1. Not sure when the picture above in your last reply was taken, but the top vent cover on the fridge vent is broke off in that pic. That is not good as rain water will get into the top of the back of the fridge compartment and create water damage issues over time, both for the fridge and the camper wood walls. If you have not replaced the top cover, suggest doing so real soon. If you are using the fridge, heat has to escape out the roof opening. Do not put plastic or other solid cover over the open roof hole when the fridge in operation. That could be a hazard if the heat cannot escape. If the fridge is off, then covering the open roof hole is OK. Just do not forget and have someone turn on the fridge.
This Camco cover will fit the older Dometic roof base.
A local RV dealer may have a cover also to fit. https://www.amazon.com/Camco-Trailer...22/ref=sr_1_2?
2. The main roof, not sure of the history or your camper, but seeing what it is there now, you have had a roof leak ('s) for some time. The fiberboard backing that the EPDM membrane was glued too, is comprised and there is little to no support to shed water off the rubber membrane. I can see the drooping of the membrane between the rafters as that occurs when the fiberboard backing is deteriorated. The fiberboard membrane can and does wick water when wet across it. The water damage will spread from a leak much greater then the one or more small water entry points. There was an attempt to slow down the leaking with some roof repair tape and possible a paint type of coating. That repair was not successful.
At this point, you may have water damaged roof rafters and some of the ceiling board may be water affected. After seeing your pics, the only repair I can see that will last, is to open up the whole roof, let is dry out, repair the water damaged wood, install new decking and a new membrane. Take extreme caution while taking the roof apart to not place a persons weight on a rafter until you know if is not rotted to badly.
3. With the amount of roof damage, odds are high the back wall of the camper has a level of water damage inside the walls. The front wall may have the same water issue. The roof leak water works into the attic and then down the corners of the back/front wall and only stops when it hits the black plastic membrane under the floor. When the water pools down in the bottom, water damage starts rotting the rear wall and floor wood. Since the corner moldings come off when doing the roof repair, you can remove the bottom few pieces of camper siding on the front and rear walls to see how bad the water damage is. And then address the damage from the outside of the camper.
There is also a moisture meter that will scan the ceiling, walls and floor without taking anything apart so you can access how large the damage is before taking the camper apart. Knowing how much damage there is, may change you mind to repair the camper or not. See here for more on the meter.
Here are some posts which may help in so show the roof and wall repair. All of the damage I see in your pics, or what you have not yet shown, is repairable. It only becomes practical cost wise to have free or extremely low cost labor. If you have work working tools and can use them in a place to allow the repair, you can do this yourself. But it will take time.
This post shows a total roof, front and rear wall repair. While it is a slide camper and is built slightly different, the methods shown will apply. It will also give you a perceptive on the size of a roof job and wall repair.
This post is more of a total camper restoration repair, but it shows how the non slide campers are built and includes, a new roof decking/membrane, front and rear wall repair. Your 2004 T2363 is built the same as this 2004 T1950 with the exception of the floor plan changes.
This post will help show how to repair walls and ceilings from the outside of the camper and not from the inside of the camper. Repairing water damage from the outside in many cases is less work/cost/time then ripping the inside apart to get to the damage.
Hope this helps and feel free to ask any questions.