Try removing all of your Parallels installation and reinstalling:
sudo /Library/StartupItems/Parallels/Parallels stop
sudo rm -rf /Library/Parallels
sudo rm -rf /Library/Receipts/Parallels*
sudo rm -rf /Applications/Parallels.app
sudo rm -rf /Library/StartupItems/Parallels
sudo rm -rf ~/Library/Preferences/com.parallels.Parallels.plist
sudo rm -rf ~/.parallels_settings
This will keep your VMs intact (in ~/Library/Parallels), but will remove everything else completely.
If it still doesn't work, there is some conflict, probably related to Qt.