Great, so you can Login to Unity 3D and you could open ccsm using the command I posted above. Now, when you setup ccsm, you gotta make sure that the following plugins are activated: Unity Plugin, Composite, OpenGL. ccsm may crash while you're starting / stopping plugins. It is really unstable. In this case, switch back to the VT and launch it again with the DISPLAY command above.
Switch back with Ctrl+Alt+F7 and activate the Unity Plugin in ccsm.
Once you have ccsm options set, switch to the VT once more and run
You *should* have fixed your desktop but the truth is that you might have to start/stop lightdm a couple times before you can see the Unity bar and panel. Or at least that's what I am seeing in a couple test PCs here.
sudo service lightdm stop
sudo service lightdm start
Now, if your Ubuntu 2D session is running OK and the 3D one simply won't run, I have to wonder if your current setup allows you to run an accelerated desktop (OpenGL). You can test it like this:
Login to Ubuntu 3D session
Switch to any VT and run:
If you get a yes to everything, your PC supports it. Otherwise, let us know in which item you get a NO.
Also, in this same VT, run
Do you see any error in the VT? If you switch to the Ubuntu 3D desktop (Ctrl+Alt+F7), do you see GlxGears running?