While I haven't experienced it, I know of a few people who have had video issues with their iMac G5's. Apple is now offering a repair program for the affected iMacs. According to Apple, a "specific component failure" may cause first generation iMac G5s to exhibit scrambled or distorted video, no video at all or no power. If this sounds like your machine, check to see if its serial number is within the following ranges:
W8435xxxxxx - W8522xxxxxx
QP435xxxxxx - QP522xxxxxx
CK435xxxxxx - CK522xxxxxx
YD435xxxxxx - YD522xxxxxx
If so, your computer may be eligible for repair, free of charge. Good luck to anyone experiencing these issues. We hope you get it sorted out.