The problem is still not solved, however here are the updates to it:
I have managed to start a multiplayer game when using my computer and my father's computer which both are on the same network. Mine is wired to the router and his is wirelessly connected. Doing so, I have used my steam account as well as my cousin's account.
I have also tried to do it with my cousin's computer and my father's, with the same problems. This leads me to believe the problem lies between the router and my cousin's computer, but I am unable to pin point anything wrong. I have done his Win7 install without changing much, like I did for my built and my father's built.
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