I found I had to pass two options to the kernel:

knoppix nowheel noapm

Leaving out 'noapm' seems to cause the computer to hang for 15 seconds or so after starting X, and then the mouse pointer remains frozen when X finally comes up. Adding noapm seems to solve this problem, although there X does boot a bit slower -- and, of course, I have no APM on the notebook.

A usb mouse works fine with the default kernel options.