Can someone help me out on how to find out if the problem is with wearesimple.dk or somewhere else?
It is wearesimple.dk. You can test it here.
Re-installing WordPress will not solve this problem. Although, it's always a good idea to update after a hack.
This hack appears to have (at minimum) injected code into your header.php file. Since that is part of your theme, it won't get updated with WordPress unless you either update the theme, manually remove the bad code, or restore the theme from a backup. Removing that code will not be enough though because you need to take steps to find back doors and such.