CONNECTION ISSUES : PROBLEM SOLVED FOR WINDOWS 8.1 (but you can try it on your version of windows)

This has just worked for me : disabling IPv6 and activate IPv4.

«DISABLING IPV6

You can disable it manually by following the steps below:

In the System Tray (bottom right of the screen), right click on your internet connection icon and select Open Network and Sharing Center Click on the connection type under Connections (usually Local Area Connection) in the right part of the window Click on Properties in the next window Uncheck Internet Protocol Version 6 (TCP/IPv6)»

link : https://support.riotgames.com/hc/en-us/articles/201752664#wq3

2015/02/25 edit : A few days ago, i reactivated both IPv6 and IPv4 because i had fps problems since i had desabled IPv6, and now everything is back to normal.