Its good that you still have any converter at all and that its still seems to be running the AC devices like the micro, air and outlets.
I assume your Roo has a WFCO 8955 converter. Here's the manual
for you. In answer to your question about checking the converter, pages 7 and 8 explain how to check the converter with a multimeter. Electrical diagnosis can be tricky so good luck and let us know how this turns out.
But before you do that, the lights and fans are 12volt so the simplest thing to check first is that system:
Check the fuses in the converter (right side of converter panel when you open it).
Battery - What is the charge you measure with your multimeter?
Check the inline fuse going from the positive battery terminal to the converter itself (usually found under the trailer on the street side).