I have reached the end of SigmaTel soundcard knowledge. I happen to have the same issue on my laptop, which is my school machine, and my desktop, which is my home machine. Both being Dell, both having SigmaTel soundcards. Both not giving me the option of StereoMix for recording. I have tried the suggested drivers on both machines. When I updated the driver on the laptop it worked for about 5 minutes then the sound crashed and there was no sound at all. I rolled back the driver, and was back to square one. On the second try of updating the soundcard driver it worked for a few minutes, then crashed the sound. I have had no luck with the desktop at all.
I guess my next step will be to purchase a different soundcard for my desktop. Is there a solution for the laptop?