You can try DT&T services to get a replacement board installed at DT&T service.
http://www.dttservice.com/iMac.html
But I have a unit that came in from a client that had the board replaced by Apple and it failed after a year. The G5 iMac is really a waist of money. Would suggest cut your loss and buy a new intel iMac. The unit is strong and reliable.
There is a kit you can get to replace the bad Capacitors on the logic board which is most likely the problem but it is hit and miss. Here are the instructions:
http://www.jimwarholic.com/labels/iMac_G5.php
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