Suggest the various cheatcodes;
acpi=off
vga=normal

could also try the copy image to HDD cheat codes, (only if you have somewhere to store the ~700MB on your HDD)
Examples (hda1 is the 1st partition on 1st HDD - change/alter accordingly);

knoppix tohd=/dev/hda1 Copy CD to HD partition and run from there
knoppix fromhd=/dev/hda1 Boot from previously copied CD-Image

Insert -> 26 after knoppix, for kernel2.6 (ex knoppix26 tohd=/dev/ha1)

Copying and Booting from HDD will eliminate any flaky CD/DVD drive issues (as long as the 700MB is copied over correctly) - and booting from HDD will result in faster performance - plus you'll free up yet another Optical drive (once booted, you can remove the LiveCD)

Also note in version Knoppix 3.6 - the default Kernel is still 2.4, while 2.6 was still "experimental" at that time (though I've used it on older hardware)

Try a newer Knoppix version - your ATi Drivers may be the issue