Yes, netcardconfig will surely do it... which is available from the Knoppix icon on the Desktop's startbar(either quicklaunch or popup Kmenu.) No to DHCP as well. I use it a lot myself. Since the menuitem has changed from Knoppix 5.1.1 in 5.3.1... I'll hold of on the directions to find it... and say you can run netcardconfig from the K popup menu, and pick "Run Command", and then type in netcardconfig. It will allow you to enter the information manually. You would need to know what to say.

IP address:192.168.10.10
subnet MASK: 255.255.255.0
default GATEWAY 192.168.10.1( maybe 0.0.0.0 will not be rejected) though interesting to know if setting it to 192.168.10.11 works well.
DNS server 192.168.10.1 (same here for 0.0.0.0)

IP address:192.168.10.11
subnet MASK: 255.255.255.0
default GATEWAY 192.168.10.1( again... maybe 0.0.0.0 will not be rejected) and/or maybe setting this one to 192.168.10.10 or 11 if 10 causes a loop.
DNS server 192.168.10.1 (same here for 0.0.0.0)

This really depends on what you want to do once connected. If ping works, and you have setup the ssh daemons
(started by the root user executing /etc/init.d/sshd start) you should be able to do some basic things. If you get a router... you could use DHCP and save yourself a lot of troubles. Even a cheap one will do that for you. Harry is right. You should have one.