no so confident about this answer, just a wild guess, but have you tried going into the BIOS and checking the sound card is enabled.
When the computer turns on look out for a message that says something like press <DEL> <F12> <F11> to enter BIOS/SETUP
When your in there use the arrow keys / tab button to navigate and look for something that says AC97 or onboard sound, or anything that hints at sound and check its turned on.
Other than that, as strange as this sounds, try plugging in some headphones into your machine and seeing if it says the audio device is available (newer windows/drivers can detect if speakers are plugged in, it may be this that is faulty, this may find it out)
Another option to consider is to download Ubuntu (linux) just google it, and burn it to CD/DVD. You can use it to load up linux onto your computer (it runs off the CD, it doesnt touch your files)
Ubuntu will automatically install sound drivers when it loads, see if you can make it make a sound, if so you know its windows thats wrong. It might be worth reinstalling windows or A final alternative is start the computer in safe mode (hold f8 just before the Start Windows screen shows, if in doubt, turn the computer on and just hold it) when in safe mode go into Start > Right Click Computer > Properties > Device Manager and then delete all references to your soundcard, restart and reinstall your soundcard.