Good afternoon sophie2525,
Welcome to the Apple Support Communities!
I understand you are having issues opening iMovie. What operating system do you have on your Mac? (Click on the Apple menu, then click on About this Mac.). What version of iMovie do you have? (Open Finder, click on the Applications folder, right-click on iMovie and choose "Get Info").
If you press and hold the Shift key while you click on the iMovie icon in the Dock, the application will open without opening any projects. There may be an issue with one of your recent projects.
If the issue persists, try deleting the iMovie preferences, by pressing and holding the Option and Command keys as you click on the iMovie icon in the Dock. You'll see a dialogue box appear that states: "Do you want to delete the preferences? Deleting the preferences will reset all application settings to their defaults. Libraries/Documents will not be affected." Click the "Delete Preferences" button.
If iMovie opens for you, then there may be a problem with a photo or a title or a video clip you used in your last project. Please reply to this thread with an update regarding the questions I've asked, and the actions you've taken, and we'll continue to troubleshoot this with you.
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Take care.