I would suggest the following. I suppose that you use your HDD install of Knoppix.
Boot the Linux 3.0.4 kernel. Open a terminal and issue
Code:
sudo lsmod > /home/knoppix/lsmodules-3.0.4.txt
Reboot the system, but now use the Linux 3.0.4-64 kernel. Open a terminal and issue
Code:
sudo lsmod > /home/knoppix/lsmodules-3.0.4-64.txt
Then you can compare the two text files and try to find out whether one kernel module was missing when you used the 3.0.4-64 kernel.