Solution 1

RESTORE "My Document" folder to default name and location.

1. Right click on My Document folder
2. Click on "Properties"
3. Go to "Location" Tab
4. Click "Restore Default" and "OK"

Solution 2

The black screen after patch happens when your fonts_en_SG.swf or fonts_en_MY.swf is not being patched completely to the game. The size for both the files are as followed: 

fonts_en_SG.swf - 86, 856 KB
fonts_en_MY.swf - 70, 030 KB
fonts.swf - 15, 030KB

Hence, please ensure you are having the complete files in the LoL folder:

C:\Program Files (x86)\GarenaLoL\GameData\Apps\LoL\Air\css

If any of your .swf files is incomplete, please download the files at this link and replace the files in the folder:

C:\Program Files (x86)\GarenaLoL\GameData\Apps\LoL\Air\css