Well, a friend put me onto this:

http://www.damnsmalllinux.org/wiki/i.../Boot_Floppies

So, I burnt DSL (which is based on Knoppix) onto a CD, made this boot floppy and tried that.

Bingo, the machine worked - albeit with a horribly distorted GUI. Unfortunately, it couldn't mount the SCSI drives.

On a hunch, I tried putting the full Knoppix CD in, but using the DSL boot floppy and it loaded, although then I found that KDE wouldn't work. However, it was largely irrelevant because the console told me I still couldn't mount the SCSI drives, anyway.

So while it didn't work on this machine, the theory is still sound for a computer that refuses to boot from CD.

Thanks for your help, folks.

(Incidentally, I found another way to get the data, in the end.)