well, to check the drivers, go to the start menu
run the 'x64 information' if possible.
Click the 'save information' button and remember where you saved the .txt file.
Upload it here, by using the go advanced button.
That'll tell me if you need to update, as well as what to update.
Also, you can try doing this too:
harddrive/Program Files/League of Legends/RADS/projects/...
delete the two folders 'lol_game_client' and 'lol_game_client_en_us'
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 in a custom Proving grounds 1vno one.