Apple doesn't replace motherboards because of leaking capacitors anymore. The machine in question is now 4.5 years old and did not have Applecare. According to http://www.apple.com/support/imac/repairextensionprogram/

The iMac G5 Repair Extension Program for Video and Power Issues applied to first generation iMac G5 computers that had video or power-related issues as a result of a specific component failure.

As of December 15, 2008, this program is now closed.