So, the issue here is that the League client will not patch if you're in queue/lobby unless you close and reopen it. It may, however, start a repair - which means that there were files corrupted in your League installation.
You would not have been given a 20 minute queue for one leave. You wouldn't even have been given any queue if this is the only game you left. For you to get a 20 minute low priority queue, you must have a history of leaving, AFKing, or quitting games in the middle of them. Even if all your issues are technical, it is still your responsibility to ensure your computer and client are not corrupted and both are functional for the game. Regardless of the reason behind the leave/afk, it still wastes your teammates time, and as such you still will have to serve the punishment.