Update regarding this, at least for some of us (NA PC players at lest):

For some the issue was that we registered our game codes, but never got the early access / pre-order bonus codes, or it would give an Error 3 when trying to submit it. SE just fixed that issue (about 15-20 minutes ago) and if you go in and redeem your game code now, it should accept it, give you your Early Access code (20 digit code) and allow you to activate it. After that login for the game should work.

Just did that myself and was able to login just fine.