[CLIENT] Game won't start - Kicks me back to client after Champ Select with "Reconnect"

Ever since the last patch, my client has had occasional issues connecting me to games.

I would Accept the match, get through Champ Select, and just after that, when the loading screen would come up, shortly after, it would disappear, with my client popping up showing me the "Reconnect" button. However, I can't connect no matter what I do.

Before, a restart would briefly fix the issue. Shortly after, the Hextech Repair Tool would, as well. Now neither of these solutions work. I've disabled my firewall (even though League has exceptions - I'm running Norton Security), and THAT isn't working.

The game doesn't seem to matter. This has happened while attempting to start Normal (Draft) games and ARAM, I don't dare touch Ranked while this is going on. It seems the only game type I can load is Practice Tool, but once I load that, up until now, it seemed to correct the issue. Now THAT isn't working.

While trying to play with friends tonight, they pointed out this occurs once the game STARTS. I get to about 99% on the first attempt, and then I'm booted from the game, with no ability to reconnect (at this point I get booted out before I even get to 25%.

EDIT: I've now attempted a full reinstall and this problem persists.