You could troubleshoot this, go back to the defaults, or change to a desktop that does what you want: see links below.
Which version of Ubuntu? The current version (11.10 Oneiric) uses Compiz by default so you would not have to install it.
Was what you installed the Compiz Config Settings Manager (CCSM)? You would need it to enable the cube.
For an immediate login you can probably still login to unity 2d (on Oneiric) or Ubuntu Classic (11.4 Natty). Options are next where you type your password in (Oneiric) or at the bottom of the screen (Natty), assuming you have not changed the login theme.
Once logged in you could try running CCSM and checking that the Unity Desktop plugin is enabled.
For either Oneiric or Natty you could try the solution here:
If its a pre Natty version, you should still be able to login without Compiz, but I cannot remember what you should choose.
If you are using the Unity desktop (default on 11.04 and later) or later it is best not to mess about with Compiz settings unless you are willing to risk having to solve problems as the Unity desktop relies on some Compiz settings. see [tuxgarage.com
] which also links to a page with some possible solutions. If using Unity, CCSM is a geek tool for those willing to mess around (which is why you need to install it separately)
If you want the desktop cube, or to customise your desktop in other ways, you probably should not be using Unity which is the least customisable Linux desktop I have tried - it works very well as it is (I like it), but your choices are restricted.
For that case would suggest Kubuntu. You can add Kubuntu to your existing Ubuntu install by installing kubuntu-desktop, either from the installer (Synaptic or Software Centre), or by switching to a terminal (which you can do with Ctl-Atl-F1 ) and typing:
apt-get install kubuntu-desktop
Incidently, Ctl-Alt-F7 should get you back to the GUI screen from the terminal.
Unless your hardware is old or low powered Compiz should work . It works (OK rather than well) on my netbook.