Hello chattychatty,
Thanks for using Apple Support Communities.
I understand that iMovie will quit whenever you launch the application after trying to share to the Theater. To get started with troubleshooting this issue where iMovie is unable to open, I'd like you to please create a new iMovie Library, and see if iMovie opens with that new library:
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Choose File > Open Library > New.
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In the Save dialog that appears, type a name for the new library, and navigate to the location where you want to save it.
The default location is the Movies folder in your home folder.
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Click Save.
A new library is created in the location you chose, and a new, empty event with today’s date is created.
iMovie (2013): Work with multiple libraries
If iMovie does open in the new library, then we know there's an issue with your existing library. The good news is that your information is not lost, since you are able to move your projects and media:
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Connect a hard disk that contains the target library to your computer, or copy the target library to your computer.
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Choose File > Open Library, and choose an option from the submenu.
You can choose from recently opened libraries at the top of the submenu, locate an existing library on your computer, or create a new library.
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The selected library is opened in the Libraries list, with the first event selected and its contents displayed in the browser.
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In the Libraries list, select the event that contains the item you want to move or copy.
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In the browser, select the item you want to move or copy.
Note: To select multiple items, hold down the Command key as you click the items you want to select, or drag a selection rectangle around the items.
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Do one of the following:
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To move items between events or libraries: Drag the clip or project to another event or library.
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To copy items between events or libraries: Option-drag the clip or project to another event or library by first starting to drag and then holding down the Option key as you drag.
Please report back with your findings!
Take care.