You should go ahead and try this solution from the Wrenchmen Toolbox:
I get a RADS error / Could not to connect to HTTP server / PvP.Net Patcher Kernel stopped working
Close out your game/patcher, hit ctrl+shift+esc and make sure all instances of LoL.Launcher and League of Legends are gone, then restart the patcher process and let it sit.
Go to your Riot Games/RADS/System folder under your default install path, right click and run the rads_user_kernel.exe file and run as Admin.
Try deleting your LoL_Air_Client folder (the default install path for this folder is c:Riot GamesRADSProjects) and then repatching.
See this article, about changing to a public DNS (Windows) (https://support.leagueoflegends.com/entries/26932010-Troubleshooting-Connection-Issues#wq4) (Mac) (https://support.leagueoflegends.com/entries/28732434-Patching-Issues#mq12)
Hit the Windows button and in the search bar type "cmd" and hit "OK". In the new window, type
netsh winsock reset
then hit enter and restart your computer.
Replace /RADS/system/rads_user_kernel.exe, with this file (http://l3cdn.riotgames.com/releases/live/system/rads_user_kernel.exe)
Try installing Microsoft Dot NET Framework 4.0 (http://www.microsoft.com/download/en/details.aspx?id=17851) and Dot NET 3.5 (http://www.microsoft.com/en-us/download/details.aspx?id=21)
Try running through the RADS solution in this video (http://www.youtube.com/watch?v=__DSdqE-Hao)
Regards,
Corta