First thing first, I would reinstall it, or make sure that you have an updated version. It sounds so miniscule, but it usually does the trick. If that does not work, I would contact Skype technical support.

Before doing so here is the standard list FYI:
To make a video call, you and the person you are calling will need:

• One of the following:
  • Skype 4.2 for Windows or higher
  • Skype 5.0 for Mac or higher
  • Skype on your TV
  Make sure you are using the latest version of Skype.
  
• A high-speed broadband connection.
• A webcam.
• A microphone and speakers (built-in or separate headset with microphone).
• If using Windows, a DirectX 9.0c compatible video card.