This is happening to me, too.
I try to start a custom game, and the League client will minimize after champ select, but upon clicking on the League window, it says that I am in a game that is currently in progress (similar to the window after you leave a game - with Zileas and Anivia, giant canyon, blue tones). A reconnect button is available; upon pressing it, League minimizes again, but the process just loops.
The same happens if I log back out and log back in - it says that I've left a game in progress (even though it was a custom game created by myself, with nothing but bots). It expires after a while (I've come back after a few hours), but I've had no luck in actually starting a game.