Have you tried:
1. Try running as an admin by right clicking on the executable and selecting "Run As" and "Administrator", or by using the lol.admin.launcher.exe
2a. Delete everything inside the your RADS downloads folder (Default Path is, C:\Riot Games\League of Legends\RADS\downloads) AND
2b. Delete everything inside your RADS solutions folder ( Default Path is, C:\Riot Games\League of Legends\RADS\solutions)
2c. Restart your computer and repatch
3a. Delete the lol_air_client folder in your RADS projects folder (Default Path is, C:\Riot Games\League of Legends\RADS\projects) AND
3b. Delete the lol_air_client_config_na and the lol_launcher folders inside the RADS projects folder.
3c. Restart your computer and repatch
4a) Go to your Riot Games projects folder and open the folder with the number for the latest release (Default path is C:\Riot Games\League of Legends\RADS\projects\lol_air_client\releases\0.0. 0.###) Find the folder with the highest number (currently 0.0.0.176 as of 8/6/12)
4b) Delete the following files:
4c) Then open the Deploy folder
4d) Delete the following folders/files:
- lib (folder)
- ETA-INF (folder)
- mod (folder)
- lolclient.exe (file)
- lolclient.swf (file)
- locale.properties (file)
4e) Restart your LoL application and allow it to repatch
5. Double check your anti-virus settings and exceptions for League