Well, like I said before, OS X is a "multi-user" system. Now I don't know your system set up, but to try and test to see where the problem lies, create another user account on your machine. In the System Preferences panel go to Users. Switch on User Login if it asks you. The create a new user, following the instructions it gives you. Log in as this new user, and run ICQ. If it works, then it suggests a problem with the preferences in your user area, and not a problem with OS X.
If ICQ doesn't run in this new User Area you created, then it suggests a problem with OS X, and a re-install may be necessary. But re-installing OS X can be a very very troublesome proceedure, so only do it as a last resort.
Follow these instructions, and let me know what happens. If you need any help, let me know, or consult the OS X help manual for info on setting up multiple users