Check out this list of things to try:
How do I trash the iMovie Preferences File? and Why?
Here's what worked for me and a bit about my situation:
--Logging into another user account, iMovie opened successfully.
--Last thing I remember doing in iMovie when it was working was exporting to Youtube. What's the last thing you remember doing?
--RESTORE your "iMovie Library.imovielibrary" from Time Machine. I restored from yesterday before I worked on that movie. This was my solution. Somehow the library got corrupted I guess. ...imagine if the only reason I chose Mac over PC five years ago was to ditch Windows Movie Maker for iMovie-- now this gets problems even more frequently! What's up with Apple 2014?