Ubuntu hangs at purple screen
Well AMD Radeon graphics cards (especially the recent ones) are difficult to use with Linux. It happens exactly the same with my AMD Radeon HD6850, until I install the FGLRX proprietary driver package.
To install it, you must go into the Recovery Mode. To do that, hold SHIFT at startup so the GRUB menu is displayed, choose Ubuntu Recovery Mode after that. Choose to mount the disk as read/write, then drop to the root shell with networking (this is very important).
Then do the following commands once you're dropped to the root shell:
sudo apt-get update
sudo apt-get upgrade
sudo apt-get install fglrx
sudo aticonfig --initial
sudo reboot
If everything worked, you should be fine and see the desktop after this.
There is a Way Easier Fix...
Just enter "e" after GRUB loads
Then delete $linuxgfxmode
from like the 3rd or 4th line down and replace with nomodeset
Winner almost everytime on 11.10 and 12.xx apparently.