I get this same issue when the game is ending and I press ALT + F4. (To clarify, this is just to save a few seconds from waiting for the game to close itself as the match is ending, not ragequitting.)
This is a good way to deal with it:
If you able to open a command prompt when the screen is frozen like this, type this and hit enter:
taskkill /F /IM "LeagueClient.exe"
This command immediately kills the League of Legends process.
To do this by button press:
Assign a button combination like CTRL + ALT + SOME_KEY to the above command using a .bat file and Windows shortcuts.
You can then reconnect from the client.