Well, my friend the Mac tech, who has a lot of experience with the USB 2.0 eMacs (the variant after yours), looked in on the thread and did not see anything that looked familiar in his experience.
He had two questions:
1) Has anyone smoked tobacco (or, I guess, even "whacky tobaccy") around the computer?
2) Has there been a history of "dirty power" in your area, i.e., blackouts and brownouts?
Ok, I'll pass on to my young expert. Not sure why he asked about smoking but he's been inside a lot more macs than I.
Sudden power cuts have historically been tougher on hard drives than other components, alsyhough I suppose that could have a effect on the power supply. However, power supply probloms don't tend to be intermittent.
Can we clarify one thing: when the screen goes black, does it come back on a some point without requiring a restart?
Yes, it just pops back into life and everything is how I left it. It's just the screen shutting down with everything still on in the background. Sometimes the blackout lasts only a minute or two, other times 20 mins or so. Some days it runs for hours without a blackout... which is why I haven't given up on it.