Before removing Compiz you might wanto to try and reset it
1.Press Alt + ctrl + F1
2.Login using your username and password
3.Reset compiz by executing
gconftool-2 --recursive-unset /apps/compiz-1
4.Reset unity , by executing
5.Optionally you can reset launcher icons by executing unity
6.Press Alt + ctrl + F7 to get back to login screen. However I recommend a restart by executing
sudo reboot. Let us know if it worked.
Cerdits to Web-E
To remove compiz and compiz packages type this in a terminal:
sudo apt-get purge compiz compiz-plugins-main-default libcompizconfig0
Warning: Removing compiz also removes the packages unity & ubuntu-desktop.
Warning: Removing libcompizconfig0 also removes ubuntu-tweak.
Thus you will lose the ability to log into the unity or unity-2d desktops.
More info here: How can I remove and re-install Unity?
And here: Ubuntu 12.04. Compiz Failure. Computer has nothing to use