I have the exact same problem as jonallen23. My laptop is an HP Compaq NX6125 (which is certified to run Linux) AMD 64 with 1GB. The boot failure only happens on Knoppix 5.1 DVDs or CDs. I have also verified that the Knoppix DVD boots on an Intel x86_64 2x2 (Woodcrest) system. Additionally, Knoppix 4.0.2 boots with no problem as does the Ubuntu and gparted live CDs.

I've used a number of boot options, such as failsafe, nosmp, libata.atapi_enabled=[0,1], debug, expert,...

I use Knoppix during Linux installfests as well as when teaching Linux at a local university. For that reason it is important for me to be able to boot a live Linux CD/DVD. The reason I prefer Knoppix to other live CDs is that Knoppix tends to find hardware when others cannot.