Knoppix generally works fine with DHCP just by booting. There are several things that you could tell us that might help:

What make and model router? I've had no problems with Knoppix and DHCP, except for trying to boot with a Belkin router, which would not do DHCP properly with Knoppix (even though it would work with windows). The other eight routers I've personally tested it with have all worked fine.

What network card?

What version of Knoppix?

This is a boot from a live CD, isn't it? If it works from the live CD but not after an install tyhe post belongs in the HDD Install forum, not here.