Either the capacitors on the logicboard have gone bad (look for bulging, a common problem on this line of Macs) or theres an issue with the graphic chip.
[http://jimwarholic.com/2008/07/how-to-repair-apple-iMac-g5.php|Here] you'll find a guide to the capacitor problem, but be warned: lead free soldering on multi layer circuit boards is no easy task. Been there, seen it, done it, bought the t-shirt ;-)