try going to https://secure.square-enix.com/account/app/svc/ffxivsvrgst
That is the exact page you put your key into. I went there from my history (I was exploring their site earlier and found it) and it took me straight there, and I was already logged in (I assume from when I logged into secure.square-enix.com to actually get my key). So I just had to type in my key and it added to my account. Though I still can't log into the game.