With out a battery hooked up, but shore power connected, are you getting 12 volts for the interior lights? If so, you atleast know the converter is making 12v power.
Assuming the batteries are known to be good, I would start looking at fuses. Typically there will be an inline fuse on the negative side very near the battery. Secondly there should be 2 fuses in series on the converter that guards against reverse polarity if someone hooks ups the battery backwards. These are the most common fuse issues. From there I would use a multi-meter and look for voltage out on the 12v side to the battery, to ensure current is leaving the converter. If fuses are good, and current is leaving, start looking for the short.
2007 Chevy Duramax LMM/Allison
2012 Jay Flight 29QBH
2012 Jay Flight 26BH (Sold)