Have you tried unmuting it from the Volume Control Mixer?
In the system tray, click the volume icon, and a popup appears, like so:
Mixer and this appears:
Make sure that the highlighted controls are set to unmute. Neither System Sounds or Skype should be muted.
Mixer has a list of all the programs that make sound in the computer, Skype will be on the list, but perhaps under a different sound device. You should be able to click the volume icon in the system tray once (Windows 7) and see a slider for each device. so try clicking the mixer button under each device to see if Skype is hidden in one of them.
Or perhaps a device has been disabled. Try right-clicking on the Volume icon, select Playback devices, and see if any devices in the list that show up are disabled?