Note: If you can boot into Ubuntu just fine, skip to step 8.
If this is a video card issue following these steps should fix the problem (make sure you have internet):
Boot as far into Ubuntu as you can
Press Ctrl+Alt+F1 to open a terminal.
- Log in with you username and passoword
sudo apt-get update
sudo apt-get install gnome-session-fallback
(this one will take a while) Note: you might be asked which display manager you want to use, select 'lightdm'
After all that is finished run
sudo reboot now which will reboot your computer
At the login screen, click on the ubuntu logo, in the top right corner of the window, and select "GNOME Classic" click OK, and login.
8. After you have logged into Gnome Classic, open 'Software Center'
9. Click 'Edit' from the menu and select 'Software Sources'
11. Open the 'Additional Drivers' tab
12. Select the driver you want and click 'Apply Changes'
Jockey-gtk has been integrated into software sources inside the software center.
So in 12.10 you change drivers by:
Opening software center
Clicking 'Edit' --> 'Software Sources'
Opening the 'Additional Drivers' tab
Selecting the driver you want and clicking 'Apply Changes'
If the above steps don't fix the problem, then your graphics card is probably not supported.
In this case you have four options:
You can install Ubuntu 12.04 LTS (where I think your graphics card is still supported)
You can continue to use Gnome Classic
You can use Xubuntu by running
sudo apt-get install xubuntu-desktop or installing from scratch.
Or you can try Lubuntu by running
sudo apt-get install lubuntu-desktop or installing from scratch.
Kubuntu is also worth mentioning, but I'm not sure it will work without drivers. You can try though.
sudo apt-get install kubuntu-desktop