It may be a corruption of your iMovie Library or the iMovie preferences.
Try first to remove the preferences, and if that does not help, create a new library.
To remove the iMovie Preferences quit iMovie, if it is running, then hold down the options key and command key simultaniously, while launching iMovie. Keep holding down the keys firmly until you are seeing a prompt to remove the preference. Confirm.

Afterwards, you will have reset all preferences that have been set from the preferences panel. iMovie will start afterwards with the welcome screen.
When I had a similar problem, the only thing that helped was to create a new iMovie Library. Probably a corrupted project in the current iMovie Library prevented the creation of new movies. Does the problem persist, if you test in different iMovie Library? You may want to create a new library for testing.
http://help.apple.com/imovie/mac/10.1/#/mov3fa25bae7