Most likely suspects:
1. Battery
2. Fuses (at the panel or between the panel and battery)
3. Auto reset breaker, also between panel and battery. Some trailers can have one for main 12 volt power and a seperate one for slide operations. (They look like
this. They are normally installed inline in the positive battery wire, near the battery, and close to where the battery power enters the trailer. You'll need to crawl underneath to look. Some have a button for a manual reset, some will auto reset. If you have power applied to the trailer, there should be 12 volt power between the two posts on the breaker. If you have no power (battery or shore) power applied, the breaker should have continuity between the posts.
4. Bad / corroded wire connections. These can be difficult to find. While your are checking for an auto reset, also check the connection where your negative battery cable attatches to the trailer frame.
Pull the battery and take it for a load test. Many auto parts stores will do it free. While the battery is out, plug in shore power and see if you still have the issues with 12 volt power. If everything is working, that would point to the battery being bad, or dead enough to prevent power getting to other systems.
If the battery is shorted internally, it can act like an extra large resistor, drawing more power than the converter can put out. Everything from the converter could be trying to charge the battery, and there is nothing left to operate lights, radio, water pump, etc.
Quite difficult to troubleshoot over the internet. A lot of the responses are just educated guessing. Please let us know what your fix turns out to be.