Capt Garrison can you test something?
First aquire an external hard drive or 16gb+memory stick
Go to the C:\ folder on your hard drive and find the "riot games" folder, copy this to your drive.
Plug the drive into another computer and open the "riot games folder" and inside of that should be the "league of legends" folder.
Inside of this will be lol.launcher.exe and another file and a few folders.
The game should open and begin to patch on the host computer.
If it finishes successfully then plug it back into your own computer and try and launch the game/do a test match.
Please post the results