Same problem, different system...
I have a Dimension e310, Service Tag BZ51S91. I formatted my HD and then re-installed XP Pro. No sound, no audio device detected, sometimes Belarc and Everest don't even see a sound card. I reinstalled the correct chipset (I think) and tried to reinstall the Sigmatel driver from the Dell site.
I've done a LOT, followed a LOT of suggestions and if it'll help, I'll send you a list of 'em. I've even re-installed XP, three times.
I have Everest and Belarc...I've attached a Hardware report from Everest.
Thanks for all your help.