Okay, now I have faced this exact same problem myself and solved this a few days previously. My previous answer was in accordance with the standard procedure for troubles regarding logging in to Unity-3D

Apparently, the official drivers that are tested by Ubuntu are not being detected and are in effect worthless.

Here is the solution I found to the issue (quoting from another site) :

http://nerdysermons.blogspot.in/2011/11/solve-graphic-driver-errors-unity-3d.html

There are 3 suggested methods that are given in this post. I have
tried all three and the third was the one that worked for me.(That is
the option where you install the open source drivers removing all the
existing drivers). The second option actually caused my system to hang
after the Ubuntu splash screen.

The procedure given in the above site, for simplicity's sake, and for
your ease can be summarised as follows:

1. Prior to taking any of the above approach, run this command to install dependencies :

   
   
   

   sudo apt-get install build-essential cdbs fakeroot dh-make debhelper debconf




2. Install Open source Graphic Drivers (Recommended) The below command will remove all traces of Ubuntu's default fglrx drivers (if
   installed).

   
   
   

   sudo apt-get remove --purge fglrx fglrx_* fglrx-amdcccle* fglrx-dev*




3. Remove the existing xorg.conf

   
   
   

   sudo rm /etc/X11/xorg.conf




4. Reinstall the xorg.conf

   
   
   

   sudo apt-get install --reinstall xserver-xorg-core libgl1-mesa-glx:i386 libgl1-mesa-dri:i386 libgl1-mesa-glx:amd64
libgl1-mesa-dri:amd64




5. Configure xorg

   
   
   

   sudo dpkg-reconfigure xserver-xorg




6. Reboot the system

   
   
   

   sudo reboot

This worked for me just fine. Hope it works for you too.