Well, that's solved.

I managed to install BeaFanatIX on the family eMachine. It's mostly based on Ubuntu 5.10 (or at least the version I have is), so it installed and ran quite fine, but in failsafe mode. Unfortunately, it doesn't recognize the soundcard, though it's a minor problem.
KateOS is still a viable option, I just have to install it first.

Ugh, distro horror.

On the family eMachine: (400Mhz processor, 192MB RAM, 4.3GB Hard drive)

Xubuntu was somewhere between horribly slow and annoyingly slow. Even Opera took a while to load, and it took forever to startup. I went and installed Fluxbuntu, but have met some annoyances. In addition to Fluxbox not being user friendly,
Fluxbuntu having some pretty annoying pre-installed applications, and worst of all, the screen resolution being funktastic, I've decided I needed to replace it.
And so I go to Distrowatch
First try. KateOS. After quite a few errors, it doesn't even boot from the LiveCD. Working with the nice folks at the forum on that one.
Second try. BeaFanatIX. Same error as Dreamlinux and Knoppix.
(It fails to find the CD holding the OS, and drops me to a rather limited shell)
It's actually rather unfortunate that BeaFanatIX had those same issues (not sure if they're resolvable) because it looked like a great distribution for these computers.