I only installed Knoppix a few days ago so am hardly an expert, but why are you installing Alsa? It is already there in v3.2 at least. I have a sound chip quite similar to yours, which was not detected on installation (AD1980 6-Channel on an Asus p4p800-vm). However, running

# alsa_snddevices
# alsa_init

correctly configured the system and loaded all drivers (intel_i8x0 and dependencies).

There is a still a bit of a gotcha here however. For this chip/m-board sound channels 'PCM' and 'Surround' have to be unmuted/turned up to get sound out. Non-Alsa mixers like kmix do not have a surround channel, so can't turn it on. You have to use an Alsa specific mixer (e.g. alsamixer in an xterm, or gamix) which display a 'surround' slider.

Later: discovered the 'knoppix alsa' cheat code for booting the CD. Sound was configured perfectly straight away. Nice.