To all of your answers:
Yes, I have reinstalled windows, went to 8.1 and then back to 7. my old card doesn't do this, so it's not any problems with my system or the drivers.
No, I do not have another machine to test it in, sorry.
Yes, I have tried a complete driver removal tool such as display driver uninstaller and driver fusion, it did not work.
Yes, I have tried the Hitman: Absolution benchmark and the Unigine valley benchmark test, received a crash on both with some artifacts but not a lot, but that's because it's a benchmark, I think.
No, it's just not League that's the problem, I've had it on Hitman: Absolution, Guild Wars 2, Modern Warfare 2, and the newly released Titanfall, huge chunks of artifacts appeared on Titanfall, actually, even with the card underclocked a hell of a lot.