Client broken, play button perma grayed out

For the past few days, I've been unable to play League because of this bug. When I launch my client and get to the login screen, a popup saying "We have restored this installation to an older version of League of Legends. Now we'll try to patch it up to the latest version." Not that big a deal, I've seen the window before. But then when I log in after clicking okay, my play button is simply grayed out. There's no indication whatsoever that the client is patching, and waiting any length of time changes nothing. Still grayed out and unclickable. Every time I restart my client I get the same patch notification popup, and the same gray button, no matter how many times I try. I can navigate the client just fine, but cannot play any games whatsoever.