I apologise. When I've retold the story other peoples' responses are simply "contact AirBnB" as if that wasn't the first thing we did. We eventually found a place for the night, resolved the issue with AirBnB (though weeks later), and promised to do a little more forethought into our next rental.
That's OK, and I'm glad you got your housing trouble figured out. AirBnB definitely should be prepared to handle problems like this right away, but I can't say I'm too surprised that they don't.