Apple Not Interested
Having spent the last few months not only following, but being directly involved in this "story", I feel a few points should be made.
The eMacs being affected are all 1.25Ghz models, built between April - December 2004, in the USA, China, and Czech factories. All present with swollen/leaking caps, and the problems experienced are not simply video problems - the entire system freezes and requires a hard shutdown. The problem gradually worsens until you are lucky to get through startup without a freeze occuring. The only resolution is to get a new logic board at a cost of $400 to $900 depending on who you ask.
The problem was first experienced in Apple's iMac G5, which was manufactured in a very similar timeframe to the eMacs that are affected. The iMac, for whatever reasons, presented with problems very soon after they were sold, whereas the eMacs have only started to show the problems since around Dec-Jan 2006 - around 18 months after they were sold.
Although Apple did impliment a repair program for the much more expensive iMac, they have unofficially said that not enough eMac owners are reporting the problem for them to consider a similar program. I suspect that the bad caps involved will all sooner or alter fail, but sadly a lot of people in the mean time have a large white paperweight sitting on their desks.
I myself tried talking to Apple Australia about the problem, pointing out the thread on Apple's Discussion Forum with many thousands of "hits", but they were not interested. I thus decided to try a different approach, and emailed
s_jobs@apple.com with a polite query about the matter. Apple Australia then contacted me and agreed to replace my eMac's logic board after it had been examined by an Apple repairer.
I suggest anyone with an eMac 1.25 open the inspection hatch on the belly of the computer and check out the capacitors that are visible near the RAM slots. If you are already having problems, call Apple, post on the Discussions forum, and email Steve.