Lucio has a perfectly valid answer in the comments, I think, that would be a good approach. This is more a backup should his approach not work. There is another thing you could try: logging in as the default user on the tty terminal and removing the Compiz configuration files there.
Note that you should be able to return to the default interface at any time by pressing Ctrl+Alt+F7
Boot your computer and continue till where you get stuck. Try logging in to the first tty by pressing Ctrl+Alt+F1. Log in with your normal user and password. Then try what Lucio suggested:
cd /home/USER/; rm -rf .gnome .gnome2 .gconf .gconfd .metacity .compiz-1 .config/compiz-1 .config/dconf.
If you can remove those folders but it does not help, you might want to try to reset the Unity profile completely. For that in Ubuntu 12.10, follow the answer given by Mahesh in How do I reset my Unity configuration?