I've now tried a third mouse: Kensington Pocketmouse Pro (2-button, USB, wheel, optical) and still no cursor.

When booting, I get these lines:
(for the Logitech) Mouse is ImPS/2 Logitech wheel mouse at /dev/input/mice
(for the Kensington) Mouse is unknown device 047d:101f at /dev/input/mice
(for the Memorex) Mouse is DSC Communications Unknown Device 1166 at /dev/input/mice
The Logitech mouse at least should work but the cursor remains invisible no matter what I try.

I've tested all three mice with and without the "knoppix wheel mouse" cheat code.
I tried the Logitech PS/2 with no USB ports in use at the same time since someone mentioned there might be a conflict.
Rebooting was done each time with the mouse to be checked already attached but I also tried hot swapping.
Somehow, I doubt that trying other mice will make any difference. There has to be something else going on.
I put the same Knoppix DVD in a laptop and it gave a normal cursor that was controllable by the touchpad.
Looks like the DVD is ok.
Any ideas on something else to try?