You can probably resolve this by removing some Address Book preference files rather than deleting your Address Book application.
First turn off Synchronize in Address Book Preferences if you can.
Next restart Address Book and try to export everything to your Desktop.
I have had a play and found my Address Book preference files. In the following ~/Library is the Library within your Home folder. Any numerals may differ on your Mac. Quit Address Book before doing anything with these.
1 - Display details and things set in Address Book Preferences
~/Library/Preferences/com.apple.AddressBook.plist
2 - Has no data - not sure what this does
~/Library/Preferences/com.apple.AddressBook.abd.plist
3 - Has last sync date - may have more if I used sync
~/Library/Preferences/ByHost/com.apple.AddressBook.sync.000393735c06.plist
4 - My contact details
/Library/Preferences/AddressBookMe.plist
5 - Individual addresses and groups stored as separate files within:
~/Library/Application Support/AddressBook/Metadata
6 - All of these addresses are are also in this single database:
~/Library/Application Support/AddressBook/AddressBook-v22.abcddb
- If you wish to remove all addresses drag both 5 & 6 to your Desktop.
- If you wish to reset preferences drag 1 your Desktop.
- Removing 3 may resolve sync issues but I am unable to test this.
- If you wish to reset everything drag all except 4 to your desktop.
Apple has an interesting page at: http://support.apple.com/kb/TS2481
I hope this helps.