It happens. After an update, the next reboot you find Unity doesn't load up as it should. Even if you're using the open source drivers.
So here's what to do (in a terminal):
~$ dconf reset -f /org/compiz/
~$ unity --reset-icons &disown
Unity should load immediately. Launcher icons will be reset to Unity's defaults, so you'll have to re-customise them. This includes your workspaces if you use more than the default one workspace in Ubuntu 13.04.
Update: Another possible solution is to delete .Xauthority in your home folder. I had to do this after doing a clean install on an SSD before Unity would load.
~$ rm .Xauthority
The above commands were obtained from Ask Ubuntu.