Have you ran slackpkg update since you installed Slackware 14? If not then do the following if you have a decent internet connection.
edit /etc/slackpkg/mirrors and uncomment one of the slackware64-current entries
edit /etc/slackpkg/blacklist and comment out aaa* and the kernel entries if they are not commented out with the # sign.
edit /etc/modprobe.d/blacklist.conf and remove radeon or comment it out with the # sign
uninstall the amd driver if it is already installed then reboot, may have to use the nomodeset option.
as root run
If asked about new config files, Overwrite since this is still a new install
rerun lilo if asked to do so
reboot try it without the nomodeset option first.
This should get you current on updates. Then we will start again with getting your graphics card working.
If you run into problems while updating just let us know, It won't be the first time problems cropped up while updating Slackware64-current.