How can i register the game i bought from gog for paradox forum?

Go to your library, click on the game and open the dropdown menu by clicking on "more". Then select "serial keys". See here.

There is no "serial keys" in dropdown menu.

Try this link:

https://www.gog.com/account/refresh

Thank you very much, i found the cd key. But now there is another problem, i redeem the code in paradox but the game doesnt show up in "my games" section, and i cant still see the forum. Any solututions to that also? :)

Just made an account to have a look. I used this link to redeem the key and then selected "Hearts of Iron III" as my game of choice. (collection and TFH don't work) It did indeed not show up in my Paradox account but it showed up when I went to the forums, picked my username and looked at the forum account's "Owned Items" page. I then went back to the Hearts of Iron III forum and saw several more sub-forums. :)