First to check is the mainboard BIOS and that the onboard audio is enabled. Access the mainboard BIOS during the POST and make sure the onboard audio is enabled. [note: Since you added a sound card, the mainboard BIOS must be disabled for the add oncard to work.
Next is that it's possible the master volume control has been muted, though the default is "always on". open the control panel and click on the sounds and mutimedia Icon. Down in the lower right hand corner you'll see a little yellow speaker icon. If it's circle and a red line through it, it's muted. Just click on the icon to unmute.Make sure the volume level is sufficent to hear something from the speakers.
Next is a problem with the driver installation. Again, open the control panel and click on the system icon. On the system properties page click on hardware/device manager. In the list of devices, expand Sounds,video and game controllers. If there is a yellow exclamation mark on the audio codecs, drivers listed. Reinstall your drivers.
Another possibility is that the speakers aren't pluged into the right port, sounds stupid but best to always check. For your onboard audio, the audio out port is the green port, audio in is the blue port, microphone is the pink port.