I hope this helps, it worked for me on my HP laptop with ATI Raedon Graphics.
Install the below packages
sudo apt-get install build-essential cdbs fakeroot dh-make debhelper
debconf libstdc++6 dkms libqtgui4 wget execstack libelfg0
dh-modaliases linux-headers-generic xserver-xorg-core libgcc1
Additional packages for 64bit architectures (has to be installaed along with above packages):
sudo apt-get install ia32-libs lib32gcc1 libc6-i386
Remove old fglrx drivers
sudo apt-get remove --purge fglrx fglrx_* fglrx-amdcccle* fglrx-dev*
sudo rm /etc/X11/xorg.conf
sudo apt-get install --reinstall xserver-xorg-core
xserver-xorg-video-intel libgl1-mesa-glx libgl1-mesa-dri
libgl1-mesa-glx:i386 libgl1-mesa-dri:i386
sudo dpkg-reconfigure xserver-xorg
Then Reboot
sudo reboot
Downloading and building ati driver package
Download the driver from Official ATI Driver
cd Downloads
Now extract the ati driver in the current folder i.e. Downloads folder, then
sudo sh ./amd-*.run --buildpkg Ubuntu/raring
sudo dpkg -i fglrx*.deb
sudo aticonfig --initial -f
sudo reboot
If compiz/unity is not starting then, switch to terminal and type the below commands:
cd ~/.config
rm -rf compiz-1 dconf gnome-session
It worked for me, I hope it works for you as well
Test :
You can test, whether the drivers installed by issuing following command on terminal
fglrxinfo
Testing Speed
fgl_glxgears
Uninistall
sudo apt-get remove --purge fglrx fglrx_* fglrx-amdcccle* fglrx-dev*
sudo rm /etc/X11/xorg.conf
sudo apt-get install --reinstall xserver-xorg-core xserver-xorg-video-intel libgl1-mesa-glx libgl1-mesa-dri libgl1-mesa-glx:i386 libgl1-mesa-dri:i386
sudo dpkg-reconfigure xserver-xorg
sudo reboot