Sounds like either the sound card drivers are corrupt or that the card has uttered it's last tune. But before proceeding, verify that the speaker jack is plugged into the correct socket on the sound card. I know it sounds dumb but I have made service calls in which that was the only problem.
1. Locate the newest driver software for the sound card. The manufacture is usually the best source or try www.drivers.com. You may need to turn off the computer and open the case to copy the model number from the sound card. After downloading the drivers, remember to unzip the drivers before proceding as most are in a zip file. Save them in a place that is easy to remember (example - C:\SoundCard).
2. You may update the drivers in Device manager by clicking in the 'Driver' tab and choose "Upgrade Device Driver Wizard but for best results, uninstall the card from 'Device Manager'. Follow this directory listing to get there;"Start,Settings,Control Panel,Device Manager"
3. Restart your PC. If the sound card is Plug-and-Play, it will be detected and you will be asked If you have software/drivers. Browse to the folder were you placed the new drivers and click OK. If your sound card is still functional, this should bring it back to life.
If the card is not detected, then follow this path "Start,Settings,Control Panel, Install/Uninstall Hardware" and run the Hardware Wizard. Since it was not detected during startup, you will need to point the wizard to the location of your new sound drivers.
If you still don't have sound, borrow a known good sound card (and driver software) to install. Repeat the steps above and if this sound card works, you will know that your original sound card has failed. If not, then there are software issues in Windows that is beyond this post.