1) Close the game client
2) Hit the Windows + R keys to open the run box. Type cmd and hit enter.
3) Type "ipconfig /release" and hit enter. Don't type the quotes.
4) Type "ipconfig /renew" and hit enter. Don't type the quotes.
5) Type "ipconfig /flushdns" and hit enter. Don't type the quotes.
6) Close open windows and restart the FFXIV client.
7) Hopefully you can now log in.
This has worked for me and a few friends. Hopefully it works for some of you as well. Best of luck.