I love a good mystery. My suggestions are........start with the easy stuff, and do the cheap stuff first. My first SWAG
scientific wild ass guess, is the battery or two are not connected correctly. The polarity is reversed. The battery positive is connected to the trailer ground. It is very hard to kill a converter. Disconnect all batteries. Again try to connect shore power. You can usually operate all 12 volt
devices with the converter power. Batteries need NOT be connected to use any 12 volt
stuff. Spray all fuses with wd-40 and wriggle all fuse connections.
If battery disconnected does not solve fuse open, wiring must be improper. Do you have any manual or wiring diagram for your Airstream. Post a picture of your fuses. Tell all information that ya know..... Circuit breakers are best.......