I’ve had a few problems with the iSight camera on my iMac not working in iMovie - yet working fine in iChat.
However, I’ve just been speaking to a Ray Ford from Apple Support who has been very helpful with this - and got it fixed in a few simple steps.
1. Click on Macintosh HD on the top right of your desktop (or whatever else you’ve called your Harddrive)
2. Click through System > Library > LaunchDaemons
3. Now look for the file apple.com.mio.VDCAssistant.plist - and send it to trash.
Start iMovie and that should work. 
Of course, worked for me, and it’s definitely worth double-echking with Apple support first before deleting any files.
Ray advised that there’s a good chance of there being an official page on this fix going up on the Apple site once it’s passed through legal & compliance.