If your soundcard works (I suppose it does...) then you should check a few things:
1) Does /dev/dsp exist? Sometimes you have to load extra modules (or so) in Alsa.
2) Are you using KDE or Gnome? Then it could be that a sound server like aRts or eSound is running. In such a case Audacity can not use /dev/dsp. You should stop all sound servers before using Audacity.
It can also help to start Audacity in a console and see if you can see error messages that clarify what is going on.
Eeltje de Vries