I didn't start having issues until I attempted to install the propretary drivers to increase performance for another game.
I suspect the issue is related to the proprietary drivers, because I have run the game just fine using open-source Intel HD graphics, and it still worked after I installed a generic GT 440 given to me. It started immediately after I installed a new MSI NVidia GTX 750 Ti, and got the system to boot up normally using the proprietary drivers. I am NOW having this issue after I have previously had LoL working just fine.