I had this problem two days ago. First I tried repairing the game, which didn't work. Then I deleted the folders in league to force a repatch to the latest version of the game, and that didn't work either. I completely uninstalled and reinstalled the game, and somehow that didn't help me, then my friend gave me an idea.
Long story short, I switched my region from North America to EU West on the patcher, and somehow doing so made my game work again. I don't know if this will work for anyone else, but it definitely worked for me. Best of luck.