Hello and welcome to the Discussions.
Let's do a test of the AB application by creating a New User Account on your Mac, and as that New User attempt to launch the Address Book application. This will tell us if there is a problem with the application. See:
http://docs.info.apple.com/article.html?path=Mac/10.4/en/mh168.html
If it works as that New User, then we can purge some preference files without doing anything to the application.
Also, use Disk Utility from the Applications/Utilities to Verify the hard drive -- this is different from Verify or Repair Permissions.
Ernie