Yes Knoppix will work with DHCP. A NIC is Network Interface Card. What kind of network card do you have? Is it an onboard or a PCI card or pcmcia? We need to know what chipset it uses. Have a look in windows device manager- not sure what it will tell you but surely somewhere in windows it will tell you what you have. You could boot the Knoppix cd and do this in a terminal:

lspci -v