Just to clarify, it is the same log in for both Galaxy and the forums right?
GOG.com is through the browser. Make sure you can log into GOG.com through Firefox, Chrome, Internet Exlorer, Safari, etc. Whatever you use. If that will not work, try a different browser. Firefox and/or Chrome normally work fine.
The forums use the same log-in as above. It needs to be done through the browser.
GOG
Galaxy is a front-end system. It's the same thing as the downloadable parts of Steam, Uplay, Origin, etc. It has nothing to do with the forums. Even if your log-in and password are exactly the same as your GOG.com login, logging into Galaxy will not log you into the forums. (As far as I know.)