Hey Weeper123 - first of all - Welcome to the forum, glad you found us. If you have a second, come on over to the new member forum and introduce yourself.
A couple of questions -- if the battery is charged and you unhook from shore power, does it cut off right away? Your best bet is usually unhooking and start at the battery and work your way to the converter. Using a multimeter, check the fuse at the battery. If you look at the fuse, usually they have a small tab that lets you check it without pulling it. Put the multimeter on each side, if you have +12 on one side, but not the other - you have found it. Next I would check the fuses in the converter (again without removing them). If you have no power to either side of the fuse, back up to where the +12 comes in from the battery. If you have no power on this wire - then you have a problem somewhere in between.
Let us know what you find!