I had the game running when I left to go do something. My computer inexplicably shut down...and now that I've started it up, my game is gone... I've tried restoring it in the manner suggested in the FAQ - no dice. I don't suppose there's anything I can do, is there?

That's not a good thing.

Unfortunately, most of the time when a computer crashes or loses power while the game is running, the savegames will usually be corrupted. If the recovery procedures in the FAQ didn't help, there probably isn't anything you can do if you don't have backups of the savegame files somewhere. I'm sorry you lost your game.