I had exactly the same problem like Lusavari with a slightly different Error code:

(30002)1342162975,0,5

After being away from FFXIV for about a month I reactivated my character last week but when I tried to log in I got a message saying something about being unable to connect to the game and the error code above.
I tried the usual stuff, restarting router, etc. but nothing changed, I tried to log in at a friend's and my parents' house to see if it got anything to do with my internet connection but it didn't work there either.
After searching the forums I deleted the UI settings and stuff in my characters folder like suggested by some people, but I STILL got the same message and the same error code.
I'm not so rich to be able to pay for more than one character per month so I didn't try if I could log into my other characters, but my main character suffered from the problem described in this thread, I think.
Since I haven't been logged on for more than 30 days I couldn't even post in the forums so I just checked this thread a few times a day hoping for a solution^^°

It's been about a week now and without me doing anything special it suddenly started working today.
Sadly I have no idea what the reason is (like maybe SE did something?) but I'm really happy to be able to play again and I wish you the best that soon your character will be able to connect to the game again, too!

I think the problem is related to characters being reactivated, since both Lusavari's and my character were reactivated right before the problem appeared..