If you don't yet have AppleCare, call now to log this issue. It sounds like the problem covered under the iMac G5 repair extension program, but if not you want to have your issue logged before your 1 year warranty is up.
Also, use the hardware diagnostic program that came on the iMac DVD and see if that reports any hardware problems. If so, that's all the evidence you should require to get your iMac repaired.