iWork apps won't launch

I recently restored my system from a Carbon Copy Cloner backup and everything works fine again, except that my iWork apps will not launch. I double click on the app (Keynote 6.2.2, Numbers 3.2.2, or Pages 5.2.2), and the icon in the dock bounces indefinitely. When I bring up the "Force Quit Applications" dialog it says the app is not responding.

I tried deleting the apps and re-installing from the App Store, with no change.

Any suggestions?

I am running OSX version 10.9.5 on a 7,1 iMac with 4GB of RAM.