Updating software (app and operating system) to make everything compatible often will resolve misbehaviors. You didn't mention what iMovie version and operating system that you are using.
Here are some other diagnostic procedures that you can try to help isolate the problem:
Try booting up in Safe Mode and, after everything loads,
immediately reboot in normal mode. Don't try to open iMovie in Safe Mode
because it will not do so. After rebooting in normal mode, see if the green
screen works.
If Safe Mode does not solve it, try redownloading iMovie. To
update/redownload iMovie 10, drag your iMovie 10 app from the Applications
folder into the trash, but do not empty the trash. Sign in to the app store and
open your purchases folder by clicking on your name at the bottom of the app
store side bar. You will see your purchases displayed, including iMovie 10.
Redownload/update iMovie from there. If not successful, drag your present iMovie
app out of the trash and return it to the Applications folder.
If still not working, and if you haven't already tested with
another project, try creating a new project and see if you can share out with
different media and also with the same media that you are working with
now.
Another thing that you can try is to create a new user account
(System Preferences/Users and Groups) and see if iMovie will work properly in
the new user account.
All else failing, try a System Management Controller reset:
https://support.apple.com/en-us/HT201295
-- Rich
f