The platform used to develop Met Office Desktop Widget is Adobe Air. If you don't have the necessary libraries installed, the software will not start.
To overcome this issues, download Adobe Air from the following location: http://get.adobe.com/air/
Download it and uncheck the McAffee offer, then click on the saved file from Software Informer and install it. The application will be available on the desktop.
Note: Adobe Air is compatible with Mac and Windows and apps run on both operating systems.