Ubuntu - I have sound!

It took some detective work but I found it, right at the bottom of Comprehensive Sound Problem Solutions Guide on the Ubuntu Forums.

webbca01 figured out how to get AC'97 work with the help of the second last post here and this post. Basically, if you have an intel8x0 module, you can get AC'97 working by
sudo nano /etc/modprobe.d/alsa-base
and adding this as the last line:
options snd-intel8x0 ac97_quirk=3