If I was to hazard a guess...
Your system is not a recent manufactured imac.. My guess that it is a polycarbonate or a 1st generation aluminum Imac, which are prone to developing graphic card failure due to thermal (heat & overheating) issues.
I think that you are looking at a graphic card failure.
Is the computer still under Applecare warranty? If so, then jump on Apple to deal with this issue.
I would follow Jasons suggestion to read over the tech note http://support.apple.com/kb/ts2570
But I would stop short of reloading the operating system on the internal drive, rather, see if you can pop a fresh copy of the operating system on an EXTERNAL hard drive and see if you can boot off of that. This way, you have a good chance of preserving your data (music & photo libraries) by going with a fresh install on an external hard drive.
If this fails, then you will be faced with a tough decision. Do you sink in a bunch of money to fix or replace the graphic card? Or, is it just time to upgrade and sell the dysfunctional imac for what you can get for it in a non functional condition.
I routinely tear down polycarbonate imacs, both G5's and intels that have graphic card failures. Its an involved process to deal with and you have limited options once you fix or replace the graphic card. This is why you see a lot of polycarbonates going for less than 50 dollars and they typically have the memory ram sticks, hard drives removed Also, missing are the keyboard, mouse, or power cord. At this point, Im a hobbiest and I'm gaining the experience doing the tear downs and the fixes.
Hope that helps.
Terrence.
PS. please come back and tell us what you discover. Folks that come after us will appreciate knowing how you solved the issue for yourself.
