I've got the same card and the closed-source drivers in ubuntu 13.10 doesn't work at all. No matter if you try the ones from ati website, the ones from ubuntu ppa, or the ones from xorg-edgers ppa...
For now, the only one that works is the open-source driver. If you want to get them improved there's a ppa with some fixes for them here:
First, be sure any fglrx is removed from the system:
If you installed them trough a ppa:
sudo apt-get remove fglrx*
If you installed using the .run package from ati website, you'll have to run the ati-uninstaller manually (not sure where it is, but you can have a look in /usr/share/ati).
And then, add the ppa and install xserver-xorg-video-ati or xserver-xorg-video-all
sudo apt-add-repository ppa:oibaf/graphics-drivers
sudo apt-get update
sudo apt-get upgrade
sudo apt-get install xserver-xorg-video-all