First make sure Knoppix is detecting & loading the appropriate driver. At the prompt: ifconfig -a
It should list a eth0 device. If that is not listed, then the driver is not being loaded.

If it is listed, Knoppix boots with a splash screen. At that splash screen you can enter codes which will force Knoppix to do certain things. Theses codes are known as Cheat Codes. I know that on 1 of my PCs, if I do not use a particular Cheat Code, the mahine will act bizzare and the network wont work. You may need to try:
knoppix acpi=off
OR
knoppix noapic