That seems strange at first, because SL 5.0 and 5.1-r1 both used the 2.6.31-kernel and ati-drivers-9.10. The difference was that 5.0 used xorg-server-188.8.131.521 and x11-base/xorg-x11-7.4, whereas 5.1-r1 used /xorg-x11-7.4-r1 and xorg-server-1.6.5. So my guess is that X.Org is the cause of your problem.
You could try pressing F5 at the boot menu when you boot the LiveDVD and adding one or more boot parameters to the kernel boot command (see the SL Wiki article Boot parameters and workarounds for problematic Hardware
). Try xdriver=radeon or xdriver=radeonhd to see if you have better luck with an open-source video driver for your GPU.