The GUI runs ontop of a program called X.
What you are seeing usually happens when X starts but a desktop environment,KDE in your case, failed to start.
A broken KDE installation from a broken update is probably a cause.
On one of the terminals,type "synaptic" and start up synaptic and then search for and reinstall "task-kde-minimal" or a package that sounds like that, i cant remember its exact name at the moment.