You go into your rads folder, then projects folder and delete both air clients. And the lol launcher folder. Back out and then go into downloads and delete the contents in there. Back out and go into solutions and delete the client folder there..........IMPORTANT..........
DO NOT DELETE THE MAIN FOLDERS, such as, dont delete the solutions folder, just the folders and stuff in it as an example. if you delete the entire main folder, you will delete game data and be back to square one.
After you have delete the material i have listed you reboot, after rebooting, right click your league launcher and run as adminsitrator. it will then patch.
So get that out of the way so they can trouble shoot you past those steps. Which will be the first thing they ask you to do.