A few days later and things still don't work. We did some more testing and everything fails.
I even tried another pc on which it always worked. The install was still the same.
After some research it's most likely to believe that the problem is caused by the router.
It seems that my model is known to have some trouble with online gaming.
So the next thing that I'm gonna do is buying the previous version of my router
that's suitable with my provider.