Please run through these fixes,
I get a RADS error - Could not to connect to HTTP server / Patcher Kernel Stopped Working
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, and run the rads_user_kernel.exe file, then try starting your patcher.
3. Try deleting your LoL_Air_Client folder (the default install path for this folder is c:Riot GamesRADSProjects) and then repatching.
3. See this article, About changing to a public DNS
4. Replace /RADS/system/rads_user_kernel.exe, with this file
5. Try installing, Microsoft Dot NET Framework 4.0 and, Dot NET 3.5