I had a similar problem on an old Mac Pro. I asked for help on a KDE forum:
In summary, this answer worked for me:
Try disabling compositing by pressing Alt + Shift + F12. If this causes the graphical corruption glitches to go away, then you might want to install the appropriate drivers for your system if it uses a Nvidia / ATI card/chip as they will likely work much better - and shouldn't experience this graphical distortion you are reporting.
Once you can read the screen, you can to into System Settings > Desktop Effects and make this change "permanent".