and it usually is after a case like this, it is fairly straight forward to remove the HD and connect it to another computer.
Depending on the model of iMac, it sounds as though you have an iMac G5 there, it is very easy to remove the drive, only takes three screws to remove the back cover, and then recover the drive.
(while you have the back off, and just out of curiosity, check the capacitors for bulges and leaks. This model was notorious for that and may well have been the cause of the problem)
My mothers iMac (model A1173) recently took a power hit and died (black screen, power button is nonfunctional...dead). She had docs etc. on it that she would prefer not to lose, and I'm sure that the hard drive is still completely operational. She has decided (due to limited $$) not to risk the price of the power supply and so is buying a replacement, either PC (again $$) or a refurbished Mac. Either way I would like to pull her old hard drive and recover the data. Is it possible to hook the drive to my PC and read it? I know Macs have different formatting, but are there programs that would allow this? I think recovery facilities are expensive, so we would greatly appreciate any suggestions for how I can retrieve her data.