I finally got it to work.
What I did, was follow the instructions in the readme-file for CBB/NewBB (DOH!);

Both "Frameworks" and "xoopseditor" packages are required by this module.
Plz download from:

Frameworks:
https://xoops.org.cn/uploads/mydownloads/xoops/xoops-frameworks-art.zip
orhttp://dev.xoops.org/modules/xfmod/project/showfiles.php?group_id=1357

xoopseditor:
https://xoops.org.cn/uploads/mydownloads/xoops/xoops-class-xoopseditor.zip
orhttp://dev.xoops.org/modules/xfmod/project/showfiles.php?group_id=1155

Those packages seemed to be in place already, but when I replaced the existing ones with the ones from the links and reinstalled the forum, it worked.
Maybe they were newer or there was something wrong with my existing ones.

Now I'm going to bed happy :)

Sorry about that, seems like they had some strange kind of hotlinking-protection.
Try the new URL instead.

These are my permissions, but I think it's the fact I can't Add a new forum which is stopping me?

XOOPS Version: 2.3
Module Name/Version: NewBB 3.08
PHP Version: Not relevant (afaik)
MySQL Version: Not relevant (afaik)
Web Server Software (Apache/IIS/Other): Apache
Operating System: Vista x64 (..)

A full description of the issue:
I can't sem to add a new forum to this module.
Should this button be clickable?
http://bildr.no/view/524620
Obvioulsy I get a message saying
" You don't have the right to access this forum.
If the page does not automatically reload, please click here"
when I try to go to the forum, but I that doesn't seem strange as no forum exists..


I apologize if this question is answered (or stupid..) but I couldn't find anything about it.

Thanks to everyone taking the time to read this!