The Cube is now up and running Mac OS X 10.4.5 off its original HD, and although it seems to have a case of the random restarts zapping the PRAM and re-seating the DC/DC board seems to have cured it for now.
I'll be letting it "burn in" for a while to see if I have to fiddle with the power button or try any of the other remedies. But so far everything seems to run OK.
Although it's no speed demon, it's amazing how fast a 450MHz G4 can feel, although I don't think it will hold up well if I throw my e-mail into it - Mail.app and Spotlight are likely to give it a fit.
My next priority is removing the dead PC from my closet and dismantle it, clean up the whole thing and re-cable so that the Cube can sit beside my mini (with them together taking up less than one-third of the room the old PC did).
Once I'm confident the Cube is nicely settled and that the power issues are gone, I'll toss my Snakelets environment into it - if Yaki can run fast enough on a 450MHz Cube, it is sure to be a good replacement for this site's PHPwiki.
That should take me most of the weekend, and photos will be up eventually.