Patcher stuck at 100%
When the patch download reads 100%, it distributes all downloaded files where they need to go. If your patcher has been stuck at 100% for a while, there are two steps you should take.
Run League as Administrator
Before starting League, right-click the icon and select "Run as Administrator". This will make sure League can make changes to its own files without interruption.
Temporarily disable antivirus
If you have an antivirus running, it may be preventing League from replacing old files in your installation. Disable your antivirus and let the patch complete, then enable it again.
If you're still running into issues after this, send us a ticket and we'll help get to the bottom of it.