This is an interessing bug i, for the first time, encounter.
I was logged into the league client this afternoon, and left my PC to go to work for 4 hours. When i came back, the client shown me that it couldn't reconnect me, and was suggesting me to quit instead (nothing new here for me.)
The issue is when I tried to launch the game again. I get the league of legend logo, then ... nothing. I already got this issue, and usually i go to the task manager to kill all the remaining league process, and it fix the problem. But this time ... nothing.
I watched my task manager to spot that league of legends process while I tried to launch the client, but nothing appear. I think restarting the computer would solve the issue, but regardless of this solution this is quite interessing...