Hi
If you restart your mac and depress the command+s keys you should be in the single user command line. Do you see it then?
I work at an apple repair centre and I have seen a few of the iMac G5s (PPC) come in with this issue. There is an Apple REP for affected units which I think is still currently running:
http://www.apple.com/au/support/imac/powersupply/repairextension/
If your iMac is out of warranty or you did not seek the Extended Warranty when you first purchased your model you may want to consider the REP. If your model is not covered by the REP and you don't have warranty cover then its likely its the main logic board. This is an expensive part as you are probably aware. If it turns out to be this then you could be looking at a repair bill that is more than the value of your mac.
Still don't despair. Try the suggestions already given and who knows it might 'fix' it?
Tony