- You mentioned Yorick crashes your computer.
- You also mentioned that Yorick crashes your friend's router.
_A champion or any aspect of League for that matter is unable to crash one's router. _
As for your crashing your computer, this is strange.
It's possible that you need to complete a clean reinstallation of League in order to resolve the issue. Grab Riot's Hextech Repair Tool and check both the box for 'Reinstall' and 'Clean Uninstall', then hit the Start button. This will wipe all files associated with League to ensure corruption doesn't carry over, then reinstalls the game.
http://vignette1.wikia.nocookie.net/leagueoflegends/images/d/d2/Annie_HextechSkin.jpg/revision/latest?cb=20160224210722
Let us know if your issue is resolved or not.
(Credits to Targon's Blade for the last step)