Hi, all.
Richs_Yard, when I searched for more info about it, it turned out to be a rouge program. It says here http://www.americanpendulum.com/en/2012/03/26/remove-system-check/ that it also tries to stop other programs from working properly (that explains all the trouble these days..)
Neowulf, all kinds of them. Critical errors, Hardware Problems, Warnings that my system is corrupted..
Industrial Miner, I am not good with dealing with computers, I have basic knowledge and I tried to do the thing you said about the processes, but sadly I have no idea how to recognize which is which.. I just stared at the task manager and couldn't figure it out.
But luckily I fond a lot of info on how to remove it and I followed the steps shown here http://www.bleepingcomputer.com/virus-removal/remove-system-check
I hope I did fine and that this infection is gone. Thank you all for helping me :)