#1. Uninstall League of Legends, delete all LoL folders. Leave none behind! O:<
#2. Click the start button, search up and click "Disk Cleaner" and just simply click OK.
#3. Re-install League of Legends from the official site of course.
#4. After downloading the game again, start the game up and see if it launches. If not, go to your League of Legends SET UP folder (yellow folder), click on set up and repair your game.
#5. Try starting up the game once more and lets hope it'll work.
BTW, my "kernal" stopped running. Also had a "kernal" error, I dont exactly know what it is but this is what I did and worked for me.
I also had an issue with the update after I was done downloading the game. It seemed to be stuck at 33%, I'm like WTF?! D:',
But I left it alone and went afk, came back and notice it was up and launching... (:
I guess it was repairing itself from the crash when it was stuck at 33% I guess, maybe, maybe not. I hope this helped.