Client won't start after patch

I patched the game today and played a few games. Then I heard Hextech was out on EUNE so I logged out of my EUW account by closing the client. I tried to open the client again, but with no luck. It keeps showing the League of Legends logo and then closing down. I don't know how to fix this. I've tried reinstalling, restarting my computer, running as administrator and I've checked my task manager but I haven't found anything. Some help would be much appreciated.
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