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Try re installing Adobe Air, Update your computer and graphics card. If that doesn't work there maybe a corrupt file. In that case follow the steps below. It worked for me.
1.Uninstall the whole client/game/LoL
2.Go to Start>Computer>Local Disk>Riot Games (or where ever you stored Riot Game folder)
3.Delete "Riot Games" folder
5.Fresh Start with no file corrupt
After that, the game should update fine and you should be playing again.
This is a better way than fixing something that is corrupted.