I too downloaded and installed Knoppix on a USB stick of 1GB. IT works fine on one machine but not on the other. The system it works on has an Atheros chipset PCI wireless. When the network utilities is run the wireless is detected at once and I use madwifi for the drivers from the builtin list. The wireless network are detected and the SSID is identified but the connection always asks for the WPA_Supplicant configuration file. There it is where I am stuck, suince I am already running other Linux I did not pay much attention to running that wireless with knoppix. But if anyone has an idea then it would be lot helpful. I am looking ahead to install a whole machine with knoppix in near future and put it on the home network.
I use wpa_supplicant and the directory of the .conf file for me is /etc/wpa_supplicant.conf
If that doesn't work also try /etc/wpa_supplicant/wpa_supplicant.conf