Are you sure that you didn't briefly start the vehicle (to move the vehicle a few feet or whatever) after having it operating in LP mode? That might be a path to the exact same problem that we've been discussing, and thus the solutions would apply. So maybe you started out on propane, but then briefly ran the engine for whatever reason, which switched the fridge to DC and resulted in the lock-up (and inability to switch back to LP) due to the on-board 20A fuse issue discussed in this thread. If you are completely unable to get it to run in LP or AC power modes, then your controller could be bad in some other way, as the on-board 20A fuse doesn't apply to those modes. It wouldn't hurt to verify that all power connections are tight, including the female spade sockets for the on-board 20A fuse - take some needle-nose pliers and compress them while the fuse is removed - as a debugging step.
There is an ignition signal wire (which tells the fridge that the engine is running and that DC power is available) going to the controller board. I suppose that a false "high" on that signal could cause it to try to switch to DC mode when DC power is not really available (the alternator is not supporting it). This sounds like an unlikely scenario to me though.