Hmmm, there is an known issue where if you are playing in windowed mode it won't load. You just get a black screen after the square enix logo. Is this what you are getting?
If so, it can take several tries to log in, just shut the game down and try again.
You can't find happiness until you know sadness and you can't have true laughter until you know the taste of your own tears.
Kaliska Rhele: Miqo'te Scholar.