Don did a bit of research and found that this was a pretty common problem in that series of iMac, and that it was likely to be an expensive fix. He took it in to the Apple store this morning and sure enough: the cost to repair the monitor would be nearly six hundred dollars. Clearly, though, this guy was of Nerdfighter stock, since he proved he was made of awesome: he offered to speak with his supervisor, who would be in within the hour, and see what might be done. When Don returned in an hour's time, he was told that they would do a One-Time-Only deal (since this was clearly a manufacturing problem) and do the repair for us free of charge.
YAY! While I was prepared to go with an alternate solution (Don's thought was to use it as a CPU and hook it up to a Dell flatscreen monitor), I'm so delighted that I won't have to. I love my iPony.
For now, though, I'm on the old Lime iMac. It's a much, much slower machine, but at least I have internet access. It's only for a week. Don updated all the software and set up my mail and lo! here I am, having a difficult time getting reaccustomed to the comparatively teensy, curved screen.