I've been following this one for a while whilst I tried to get my head round the question. My theory is as follows.
If you enter a dark room and turn on the light, the light will move at the speed of light until it reaches your eye. This has been measured as you say at 'the speed of light'.
Therefore, when you turn off the light, the light will recede at the an equal speed (assuming the speed of light is constant and who am I to argue?) meaning that the speed of dark is merely the speed at which light recedes i.e. the same. This is assuming that light is not subject to the Doppler effect?
Problem solved. Next.

Been working on this for Hours too. What happens then if i just close my eyes, how fast does it move then???

That may take a little longer but I reckon J-P Sartre may have had something to say about it. This is surely an existentialist question? 
Had to look that one up...................................
Existentialism is a philosophical movement which claims that individual human beings create the meanings of their own lives. It is a reaction against more traditional philosophies, such as rationalism and empiricism, which sought to discover an ultimate order in metaphysical principles or in the structure of the observed world, and therefore universal meaning. The movement had its origins in the 19th century thought of Kierkegaard and Nietzsche and was prevalent in Continental philosophy. In the 1940s and 1950s, French philosophers such as Jean-Paul Sartre, Simone de Beauvoir, and Albert Camus wrote scholarly and fictional works that helped to popularize themes associated with existentialism: "dread, boredom, alienation, the absurd, freedom, commitment, [and] nothingness".[1]