You can try to see if this is a USER issue on your Mac rather than a software issue. I do know that the App Store can get buggy.
Can you log into the App Store? Are you able to view you purchases within iTunes Account?
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How to create a new user:
http://support.apple.com/kb/PH11468
You can create a new user and then try to open FCPX. If FCPX works with the new "test" user then your issue is with the App Store App.
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This may help with the App Store issue, if indeed creating a new user results in the same problem.
http://support.apple.com/kb/TS4236