I am assuming Windows 7.
Try closing out of anything you have running (including any torrent and torrent helper apps). Disable/Modify your firewall software to allow Torrent Ports (Google FFXIV and ports), and make sure you have the latest updates/install of your video card, and DirectX. And lastly, go through the Config tool, and make sure the settings in there are valid for your system (e.g. the video resolution is something your monitor and video card can handle, and that the settings are not too high for your system)... If you have any doubts about a setting, set it lower then standard, and give that a try.
If you have to change your settings to try and get it to work, you can go back later and try putting them up a notch at a time to find the best settings you can have and still play the game.