I don't want to be banned by riot for switching from a laptop to a desktop. I have heard a while ago that when they do ban waves it detects for different log in on different machines, and since I switched to a new machine I'm a little worried.
They don't ban people for playing on different computers at all, that information would only be a small piece in an investigation in determining if you were account sharing, they'd be looking for a lot more than that.
https://support.riotgames.com/hc/en-us/articles/204168430-MMR-Boosting-Detection
Try not to infest your new computer with anime. http://www.auplod.com/u/udpoal6c174.png
Only thing I would recommend is loading up a custom game to confirm that your graphics card's settings are correct.
If you BSOD, fix whatever is causing the issue before playing an actual game.
