Couldn't log in error

I have some trouble logging into league right now even though I'm certain I got the details correct, I even changed the password and it still didn't work. I even tried to log in with several different accounts and it still didn't work even though my friend tried it on his computer and we have verified that the username / password are correct. The video link was what exactly happened on my screen.

Please tell me how and why is this happening and is there a fix other than reinstalling the game. Thanks.