Hi, I have an oldish AMD graphics card. Maybe my process to get that card to work might help or give some other ideas.
bash-4.2# lspci -vv
01:00.0 VGA compatible controller: Advanced Micro Devices [AMD] nee ATI RV620 [Mobility Radeon HD 3400 Series] (prog-if 00 [VGA controller])
Kernel driver in use: radeon
I had given up to use the proprietary flglx-driver as it kept giving me install-problems. At the moment I am using the open source driver from the kernel at its native resolution of 1280x800, and the ati-driver that comes with Slackware.
For this, I did the following:
1) installed a subset of xf86-video drivers:
bash-4.2# ls /var/log/packages/xf86-video-*
2) edited /etc/lilo.conf (after doing so make sure to rerun 'lilo' as root)
vga=773 and the rest, including all VESA framebuffer settings commented out
added the 'append=video=[native resolution]' to the linux-booting block
image = /boot/vmlinuz
initrd = /boot/initrd.gz
root = /dev/sda6
label = Linux
3) included a video.xorg.conf file:
bash-4.2# less /etc/X11/xorg.conf.d/video.xorg.conf
(plus similar files for the touchpad (50-synaptics.conf) and keyboard-layout (90-keyboard-layout.conf) settings)
4) made sure that all ati-stuff installed by the fglrx package is removed (In my, possibly outdated experience: after uninstalling the package, ati/fglrx stuff keeps lying around in /etc as well as in other places like /usr/share and /usr/src.) Reinstalled Mesa as its glx-component could be overridden by the ati-driver.
5) I do not have an /etc/modprobe.d/blacklist.conf (see ReadMe in /etc/modprobe.d/) or one dedicated to radeon to get it blacklisted
NOTE in case the kernel-driver is not good enough: it used to be possible to create slackware packages from the AMD flgrx install package; please run the install-script with " --help" to see the appropriate options for this (something like " --with package=Slackware Linux" would be the setting for that).
Hope this could help you on your way (btw ati-cards never blew up my computer like nvidia's did).
PS. Your amd graphics card is not like the linux-unfriendly optimus cards from nvidia?? if so you might need another solution altogether.