1. Close out your game/patcher, hit ctrl+alt+delete and make sure all instances of LoL.Launcher are gone, then restart the patcher process and let it sit.
2. Go to your Riot Games/RADS/System folder under your default install path, right click and run the rads_user_kernel.exe file as an admin, then try starting your patcher.
3. Try deleting your LoL_Air_Client folder (the default install path for this folder is c:\Riot Games\RADS\Projects) and then repatching.