Since last client restart, my game will not load (black screen)

League ran fine for me yesterday. Since then my laptop did some kind of download and also League's client gave me the whole "Client restarting, etc" thing … so I guess there was also a League update.

Now when I click my LoL icon all I get is a black screen or a black box on my desktop. The League icon is at the bottom of my screen but the actual box is just black. Nothing is appearing and running it as Administrator hasn't fixed anything.