Um, as opne last experiment I plugged in the "BAD" (gives S.M.A.R.T. errors on every boot) IDE hard drive as my primary and....
...it tried to boot!
OK, it gave errors, but I could now access SETUP and BOOT MENU. Turns out that the old drive has a version of GRUB on it and an old Ubuntu install. Grub runs but Ubuntu is stuffed. But that's not the point. The Media PC isn't dead after all. When I plugged the other IDE drive back in and tried to boot, it froze, just like before, so that drive is the cause of the problem. If I can find another (GOOD) IDE drive (probably at least 40 Gb) the Media PC will be resurrected.