I would honestly seek help from Customer Support. I don't have much insight into these types of problems.
I noticed you mentioned proxies and firewalls, but I didn't see you mention an anti-virus program. Which one do you have and have you tried turning it off?
Eset nod 32
I've mailed them already, NO response...
© 2014 Riot Games, Inc. All rights reserved. Riot Games, League of Legends and PvP.net are trademarks, services marks, or registered trademarks of Riot Games, Inc.