I don't know what goes on with your machine, but maybe it has not enough memory to run KDE or any heavy desktop ? If you don't know Linux : Linux has many desktops - we use mostly KDE and Gnome, then more and more often Xfce, Lxde, and since a pair of years we also use Openbox -almost standalone-
KDE and Gnome are the ones which require the more resources, Xfce less, and almost as generous in features as KDE, the Lxde is next, less greedy, and becoming more and more easy to use, with many graphical use interfaces to configure your preferences. Openbox standalone is to be left for people already knowing Linux a little.
If you want to check the memory, you could open a console and type "free" hit return, then "free -m" hit return. Please bring back the output.
If you want to test the memory, you could run a memtest (an option which is available at boot).
I would also suggest you look at what graphical driver is set : I suppose it would be radeon ? You can do this in console:
grep "Driver" /etc/X11/xorg.conf
and if you open the PCC at the Hardware>Video section, look if hardware acceleration is on : if so, set it to off (in the advanced part of that section). If hardware acceleration is on for the mouse, set it to off as well.
I also tried Alt/SysRq REISUB to try to safely shut down - no joy.
Does that mean it didn't work ? If so, you can enable it in the file /etc/sysctl.conf : the line "kernel.sysrq = " should be set to 1, this way : kernel.sysrq = 1