The login screen is available but it sais my password/login name is incorrect.
I try the same details on the online webpage and no problem. I can see that my PSN account is linked there as well.
I believe this also happened to me during the PS3 beta last year preventing me from participating.
edit 1: Wait... it worked using my username. Doesn't support e-mail as login... amateurish... but now it's complaining about lacking country of residence. Maybe you should have let me edit that in the PS4 game.. *opens SE site* ... oh I see. I already have my country (Norway) assigned. I distinctly remember facing the same problem last year with the PS3 beta as well. I would be grateful if anyone who has faced this challenge before detail their steps.
edit 2: Well... it seems like SE has a two tier system with two different websites:
http://na.square-enix.com/us/profile/edit/accounts
is the not the same as...
https://secure.square-enix.com/account/
You need to edit the identical attributes on that second site... which affects both...
edit 3: Problem was in parts the PS4 keyboard adding a space after my name was entered. This was practically impossible to see on the pocketstation sized browser window as well. This fixed my problem and I'm now updating the client proper.