It would seem that our iMac G5 will not go without the capacitor problem that so many other people have had. One page in particular says that while the official program to repair the issue ended in December 2008, they are still fixing the issue if you ask nicely. So we'll see if I'm nice enough!
If you click the photo you can see how some of the capacitors are "blown out" -- in other reports there have been ooze coming out of some of the more roasted ones, but it didn't get to that point on ours. It would seem that there are guides out there for replacing these DIY but I'm not sure I'm up to it.