First of all, please check your disk for any errors. Please run Repair Disk in Disk Utility (on your Macintosh HD). If the errors are bad, probably you need to restart your Mac and then hold CMD+R until logo appears, then you should re-run Disk Utility.
You can also try some 3rd party software for recovering the files for iWork like Stellar Phoenix Macintosh.
If this doesn't work, please open Console to check the logs or do it manually from the Terminal:
$ tail -f /var/log/system.log
and run Pages/Numbers again.
This should point you to the specific error which you can look for.
If you don't have any errors and your disk is clean, then you can try to Reinstall it via App Store:
Here's how to reinstall an application from the Mac App Store:
Open the App Store application. (It's on the Dock, or in the Applications folder.)
Hold down the Option key and click Purchases.
An Install button appears next to the missing application.
The "missing" application won't be missing for much longer. It's now downloading to your computer! When the download is finished, you'll be able to find the application in Launchpad and the Applications folder.
Another method you can try is the suggestion from this thread:
Open App Store, go to Purchases page, re-download thee apps. You will first need to drag the iWork folder to the Trash.
If you still can't download it from App Store, you can try from re-download it from torrent (you should have a proper licence).
But if you'll download the older version and it still doesn't work (which will show some missing frameworks, file images, etc.), then you'll have to do the upgrade first via App Store.
If none of above will work, try to remove cache and setting files from your Home Folder:
You can list them by the following command:
find ~/Library -iname \*iwork\*
If none of above will work, then you can try to debug wtf is going on by:
First run in Terminal dtruss command to listen for e.g. Pages execution:
sudo dtruss -fn Pages
Run e.g. Pages
Dtruss should show you some debugging stuff.
If there is too much going on, you can log it to the file by:
sudo dtruss -fn Pages 2>&1 | tee dtruss.log
To filter only file operations, you can try:
sudo dtruss -f -t lstat64 -n Pages
or the easiest way by running OSX pre-defined dtrace script:
sudo filebyproc.d | grep -i iWork
This would give you some idea what files could be wrong/missing during the start.