Have you tried deleting the relevant files, and then repairing? A repair only checks that you have the existing files. Deleting them forces the game to redownload them.
harddrive/Program Files/League of Legends/RADS/projects/...
delete the two folders 'lol_air_client' and 'lol_air_client_config_na'
Run the LoL Launcher, hit the cogwheel in the upper right hand corner.
Run a repair, let it finish, it'll download the deleted folders.
Run the game, test if you can launch and join a custom game, 1vnone.