Crashes during loading screen.
My League of Legends started crashing after the 3.9 patch, but I still think it has to do with the Dargon Mod Installer. It crashed during the loading screen before games and then it takes 1-4 tries to get it to actually load.
Uninstall the Dargon Mod Installer and stuff with it and see it it loads and if it does then that was you're problem.
Try doing a repair (top right corner of launcher) If that doesnt work, try to uninstall & reinstall.