The closed-source driver (FGLRX a.k.a. Catalyst) does not support your GPU: the last version of the closed-source driver that supported it was Catalyst 9.3 back in 2009, and that won't work with today's kernel and X.Org Server, etc. So you need to try the open-source alternatives: either a) the Radeon kernel module (see joost
's blog post Getting rid of Catalyst
) or b) the X.Org Radeon driver xf86-video-ati (see the post Re: ATI Mobility Radeon X 1700 Драйверы!
and take into account that the latest SL kernel is now 3.0.0 [package linux-sabayon-3.0-r10]).
You may find in the second case (b) you need to blacklist the radeon module if the SL kernel image was compiled to load it by default at start-up. If you don't know how to blacklist a module to stop it loading, see e.g. Re: Quit shipping nouveau with the kernel!
. you might also have to turn mode setting off (add "radeon.modeset=0" in GRUB 2 in a similar way to what joost
explained in his blog post).
I've not tried any of this as I don't use the open-source Radeon driver myself.