If you heard a "bang" or pop, and/or smelled smoke, then it's probably toast and not worth trying to fix unless you or someone you know have enough skills to find out what blew. It's worth opening it though to see if there's some internal fuse or circuit breaker or something that tripped.
But the bigger question is, how did you backfeed it? If you don't have a transfer switch and you were able to feed 120VAC into the inverter, then it seems like you could also backfeed 120VAC from the inverter into the shorepower cable, which is a safety hazard for you and for the electrician that's working on restoring campground power and doesn't realize that you energized the "dead" circuit.