This post may or may not shed some light, but I have read about this same issue from everyone and everything else more and more over the past couple days. Found this on http://www.nowgamer.com/news/2066654...002_90000.html Check it out, just a few paragraphs.

Error "2002"
This error is very similar to error 1017, except to say that FF14 has had restrictions put in place for players to try and prevent servers from becoming overcrowded and creating issues for those still playing the game.

This error will likely happen on the main menu (where it plays the famous Final Fantasy tune) and the 'Start' button will be greyed out.

You won't be able to click start and, if it doesn't become available within a couple of seconds, will mean you're unable to connect to the character selection screen.

This is in a bid to prevent too many connecting to the game and, sadly, cannot be fixed through traditional means.

However, it is also worth noting that Error 2002 can be caused by your router and the port settings. If you keep getting this error code then access your router to unblock the following ports:

UDP
55296～55551

TCP
80, 8080, 443, 55296～55551

The update functionality of Final Fantasy 14 makes use of UPnP, and so can be block by some ISPs. Though you can still download update data with UPnP inactive, if you are experiencing issues then it is worth unblocking these ports to attempt a fix.

There is no guarantee that this will help, but it's worth attempting to get back into the game.