If it is a converter, (As it appears it is) and the lights do not work, then one of several conditions exists.
1: Batteries are TOAST, I mean DEAD. and in this case I suspect SHORTED. More on this later
2: COnverter dead.. (I think not, cause if it was dead it could not blow it's fuses, however it still stands a chance)
3: Short circuit elsewhere in the 12 volt system (Suspect #2 in fact)
4: All lights burned out (Possible, not likely but possible, would not account for blown fuses)
SO, how do we test?
Step one, get some RED paint or nail polish and go to the batteries (or tape or heat shrink tubing) You may also wish to get some BLACK, same list.
Paint the wires connected to the POSITIVE battery post red
Use black on the negative wires
When dry remove the negative wires (ALL OF THEM) From the battery
NOTE: if using heat shrink start by removing the negative wires, slip some heat shrink over them and shrink it down
Then once that's done do the same on the PLUS side
Now, replace the fuses, plug in and see if the lights work and the fuse blows.. If they do. batteries are your problem
If the fuses blow, problem is elsewhere in the 12 volt system
Home is where I park it!