My guess (only a guess) those two fuses that you found the burn marks on were supposed to blow to protect the diodes in your converter/charger. Apparently, if you have 0VDC out from the converter, you won't charge your batteries. I'd suppose the fuses failed to protect against a short/reverse polarity and you fried the converter. You can buy a replacement to fit the existing power supply from your dealer or from most online RV supply sources. I'd advise, if you're not familiar with what you have and what to replace it with, it'd probably be wisest to consult your dealer with the name, part number and serial number of your power supply and let him suggest which replacement to buy. Once it arrives, it really is simple to take the old one out and install the new one.
If you want to assure that the batteries are working, put them on a 12VDC charger (wired in series) and charge them for 12-14 hours. Once they are charged, reinstall in the RV and turn on lights, check your voltage monitor, it should show 4/4 llights initially and after time (30 min to 60 min of continuous use) should drop down to 3/4 lights
Hope this helps, PM me if you have questions,