I actually wrote a pretty long discussion about this, but I got deleted and I can't be bothered writing it again..
Basically when 8.21 patch (K/DA skins patch) hit the PBE server, the client wouldn't open, I was stuck at the LoL logo on my desktop every time.
Now the patch hit the live servers and the Live client will not open.
Yes I have tried resetting my computer and my internet..
Any other suggestions would be helpful,