As of this morning, I reloaded my client and it was up to date, and I still had the problem (that was my previous post). I closed it out and a few minutes ago I opened it up, and it was still up to date. I'm in the long queue right now, so if for some magical reason it works, I'll let you know ASAP. Edit: the problem has not yet been fixed. Until then, here are all the logs I have under RADS\projects\lol_air_client\releases\0.0.0.207\de ploy\logs (keep in mind I did reinstall yesterday).
(I split it into two folders due to the forum size limit)