Roommate and I losing lp like crazy and client won't let us log in.

So my roommate and I can't play the game. We are constantly not able to load into games, with errors saying that our connection is not working and we are given options to retry or cancel. Our internet is fine - we are able to use our browsers, play other games, etc. But we keep getting this black screen after champ select, losing LP for "leaving" and then being forced into 20 minute queues to get back to the black screen. Has anyone found a fix?

Also - after restarting the client a billion times to where we have to re-login, the client does not recognize our usernames / passwords and we have to use the troubleshooter to fix corrupted files to get back into the game.

EDIT: Initiating a full repair through the client is no longer letting us log in. The client still does not recognize our username / password combinations. I've also tried resetting my password and that does not work.