The keyboard uses the MIDI synthesizer in Windows to generate notes. If you are not hearing any sound when clicking on the piano keys, but are hearing your singing when playing back, then there may be a setup problem with your computer’s MIDI synthesizer.
First, check that the MIDI is not muted in the volume control mixer (click on the Options->Audio Properties menu in Sing&See to get to the Sounds and Audio Devices control panel and then in the “Audio” panel click on the “Volume” button to open the mixer panel).
If that doesn’t fix it, you may have some problem with your MIDI output device. Check this Microsoft support page, or this one, for some suggestions.