League of Legends requires administrative privileges to install and run correctly. There are several fixes for this problem which are described below.
Make sure you have all available windows updates installed from here.
MAKE SURE YOU ARE AN ADMINISTRATOR
You can do so by following the steps described here.
Detailed instructions here.
Please note: Make sure to use the "Never notify" setting.
RUN THE GAME AS ADMINISTRATOR
- Right click on the short cut for League of Legends
- Select Properties
- Check the box labelled "Run as Administrator" under the Compatibility tab
Please Note: If you are using Windows XP, you will need to login as an Administrator.
CHECK YOUR HARD DRIVE FOR ERRORS
Occasionally, these problems can be caused by a corrupt disk fragment. To check for corruption, run a Scandisk on the drive.
REINSTALL THE GAME AS AN ADMINISTRATOR
If all else fails you may need to re-install the game with administrative rights using this guide.