One of the first steps is to boot Ubuntu in recovery mode:
Basically, you select the
Ubuntu, kernel 2.6.xx.xx-generic (recovery mode)
option in the GRUB menu. Choose the recovery mode of the kernel that is not working for you (I assume tha t is the latest, so the one with the highest kernel number combination.)
You should now get some options of which the option "Drop to root shell prompt gives you the chance to make some repairs on the command line.
For analysis you can now look at your log files:
this might help. You could attach them to your question for others to see.
You can also try to see what happens if you start the X display manager (lightdm)
One possibility is that, you use a fglrx or nvidia driver that needs to be recompiled (but again i am just GUESSING here, i know nothing of your setup).
Check if you have a /etc/X11/xorg.conf (is normally NOT there). If it is present, rename it :
mv /etc/X11/xorg.conf /etc/X11/xorg.conf.mypersonalbackup
and try again.
You might experience loss in video quality until you recompiled/reinstalled your video driver.