Turns out that when you burn your CD's with a proper CD burner (not one inside an old laptop that has bene sitting still in unknown conditions for an unknown amount of time) it actually works!
Either that or the BIOS update that I grabbed from archive.org yesterday actually made a difference.
Anyway, the one laptop that didn't want to run Linux now runs Linux, specifically Red Hat Linux 7.2 (with Gnome 1.4) from 2001, on a Compaq Armada 100S from 2000.
@StroomAfwaarts CD-R stands for Circular Datacarrier Minus Round.
This is to signify that there is a Round piece missing from the center of the Circle. Which is very useful for handling your dubbeltjes.
@lkundrak hey I just wrote what was in the .iso's filename.
https://archive.kernel.org/redhat-archive/redhat/linux/7.2/en/iso/i386/
It's on kernel.org, they should know.