nuuttiT: Ha! So it's the server gnomes in GOG fooling around again. =)
Seriously:
I've had this login nuisance about a week now. I use Linux Mint with Firefox, with HTTPS turned on when possible, on my current main computer. Seems to me though it hasn't got anything to with my settings on this machine since I've tried and faced the same problem also on different Vista, Win7 and Win8 computers.
I can just imagine all the gray hairs GOGs techies get while trying to solve this, as it seems to me that the cause might be some small change somewhere sometime last couple of months.
Anyway lets hope things go to normal soon. =)
Keep in mind that the secure connection on the front page is broken for months now (ever since the Winter Sale) - even though you start at secure.gog.com the moment you hit the "Log me in" button, the site reloads and reverts to (plain) gog.com.
In case you have HTTPS Everywhere with the GOG rules installed you won't be able to ever log in to the front page, unless you disable the rules.
The sad part is that GOG Support has stated that it's a very low priority issue that they won't look into it before they're done with other higher priority matters.
FWIW, I was able to log in to the forum at my first try today using the latest Pale Moon and HTTPS Everywhere with the GOG rules. But as I said, the store front page doesn't acknowledge that I'm logged in.
But using SWare Iron and plain http, I had to log in twice before the site acknowledged it both on the store front page and on the forum.
That's at least an indication that opening gog.com or gog.com//* and then trying to log in doesn't work properly.