The first thing you need to do is make sure that you have a Realtek card.
Download a program such as Speccy: Speccy - Download
Once you've confirmed your sound card, download the latest drivers straight from the Realtek website.
In the case of HD Audio drivers: Realtek
Now uninstall your old drivers using the Device Manager.
Once your old drivers are uninstalled, you'll need to install the new ones.
If your sound card still isn't working after confirming the make and model and installing the correct drivers you likely have a problem with the card itself. If you have an independent sound card you could try using the onboard sound instead, however Realtek is usually the onboard sound so I'm guessing that's your only option.
If you were planning on upgrading your sound from Realtek anyway, you could buy an independent card from a company like Creative or HT OMEGA. You can find good cards such as the X-FI and the OMEGA Striker for about $60 at Newegg.com
If you don't want to replace the card, you should probably exchange your motherboard for a new one after you've exhausted all of the software options and tested your speakers on a secondary source to make certain they're working properly.