Updated to Yosemite. All iWorks fail

First, try resetting Keynote; complete all the steps and in the order listed:

1. Remove Keynote version 6.5, you must use an application removal tool for this procedure to work: Appcleaner is free, I use Appzapper
2. Empty the trash
3. Shut Down the Mac (Apple menu > Shut Down)
4. Wait 10 seconds, then press the power button
5. Immediately after you hear the startup tone, hold down the Shift key,
   release the Shift key when you see the grey Apple screen
   start up will take a few minutes longer than usual as the Mac is performing a software repair
6. Restart the Mac normally, (don’t hold down any keys during startup)
7. Install Keynote from the Mac App Store

Lastly, your profile shows you are using Yosemete 10.10.2, if this is correct update to 10.10.4

Create a new account in: System Preferences > Users and Groups

if the apps now work, your original account is corrupt.

Having tried the last two measures, this would indicate a corrupt install of Yosemite. The only option is to delete the existing OS and install Mac OS with a clean instal.