Okay. I have this problem all the time, and it seems to be linked to Maestro.
First things first, let's see what happens when you get into the login screen:
On your patcher, with the button grayed out, type in " thereisnourflevel " No spaces, no quotes.
The play button will become orange and clickable.
What will probably happen; is that when you get into the login screen you will receive the Maestro Error.
In this case, this is how I fix my Maestro Errors(I get them every patch.):
First, make sure there is no League of Legends running in your processes. If there is, end it.
Go into your League of Legends folder in C:/Riot Games
Open up the "RADS" folder.
Open up the "Projects" folder.
Open up the "lol_air_client" folder.
Open up the "releases" folder.
Open up the folder that's in there. It changes every patch, but contains the same stuff. (Or open up the one that has the highest number on it. (0.0.0.236 might be it for you.)
Delete the two files named "S_OK" and "release manifest"
Open up the "deploy" folder.
Delete the "logs", "META-INF", "lol.properties", and "LoLClient.exe"
Restart your Patcher.
It will repatch the recent patch you had just downloaded.
This may not work for everybody, but at least give it a try.
Hope I helped.