has Aperture 3.4.2 worked at all after upgrading from 3.4.1?
An unresponsive user interface typically has one of three reasons - a corrupted preferences file, or broken files in the application's package, or incompatible kernel extensions or plug-ins.
Are there any diagnostic messages in the Console window, when you try to export?
Since you are saying this happens also when working from a different user account, it probably is a system wide trouble. Did you install any non-Apple applications that had installers running and might have installed frameworks or kernel extensions?
if you open your System Preferences, are there any additional non-Apple preference panes? In the User&Groups Perefereces pane, do you see non-Apple start-up items?
If you can exclude any non-Apple software, that might be incompatible with Mac OS X 10.8.2 and need upgrading, then I'd reinstall Aperture. On the other hand, if you have incompatible third-party software installations that might have corrupted the system, it might be necessary to reinstall the system.
So, after a long journey into the deep of my computer....hahaha....
Because any installtion, removing prefs etc didn’t work, I simply use Path Finder to deeply look into all (hidden) folders and search for any file, which name has written "aperture" in it. And voila, in some folders within the /Library and /Home/Librry several files didn’t become deleted, when removing Aperture. ANd guess what: After deleting of all files found and after restart I copied a fresh Aperture on my disk, make the update and it works again.
Thanks to all who want to help me.