Many Thanks Guy,
Attached a screenshot with firefox on top totally blackening out the task/upper bar, not reacting e.g. to where the minimize or close windows buttons would be, and internet explorer underneath, partly blackening out but still having clickable items in the upper bar. If windows live mail blackens out (currently it's working) then the complete ribbon disappears that would contain the reply, send, delete, move,... buttons. Sometimes also the left bar with the folders or the contact bar would go black.
I could not see any regularity in the appearance of the problem. So yes, to me it appears completely random. Not many other programs running in the background. Probably windows live mail, acrobat reader, sticky notes, and onenotes are the programs that have always been running on my machine and, thus, when these problems appear. It's a Dell XT3.
Many thanks for your help!