According to the support service tag number on your Belarc printout, your PC is a Dell Dimension 3100/E310. You'll find all the OEM device drivers for it here, for Windows XP (there's no distinction between XP Home/XP Pro as far as the drivers are concerned).
http://support.euro.dell.com/support...&os=WW1&osl=EN
I see there are two different device drivers listed in the 'Audio' category. You only need one of them -- but it must match the device you actually have.
I have no way of knowing that, but you can click the link "Help Me Choose" for guidance on this. Obviously only the correct one will get your sound working, so you could simply take a guess and if that one doesn't work, uninstall it and grab the other one. You will only get it wrong once!