I posted this a few times, but here you go.
As long as you're comfortable installing a torrent program (If you don't have one already), and do some dragging/dropping of files into other folders, do this. It's worked wonders for our LS:
1. Open the FFXIV open Beta client, allow it to get to the step where it begins downloading files. This will ensure you have the torrents downloaded on your computer.
2. Open whatever application you use for downloading torrents. If you do not use one already, I would suggest uTorrent ( www.utorrent.com ). In Utorrent, File > add torrent. Point Utorrent to the following:
Documents\My Games\FINAL FANTASY XIV Beta Version\downloads\ffxiv-beta\d96437e6\metainfo
In the metainfo folder you will find files that have the same name as the patch your FFXIV was trying to download. Select these files, and hit open.
3. Utorrent will now begin downloading these files to your computer. Based on your internet connection and security settings this should take less than 5 minutes. By default Utorrent downloads to the "downloads" folder in your documents folder. After it is complete there will be a folder called D96437e6, inside of this folder there will be a folder called patch, and inside the patch folder, there will be the actual patches
4.Copy these files to Documents\My Games\FINAL FANTASY XIV Beta Version\downloads\ffxiv-beta\d96437e6\patch
5. Open FFXIV, it will try to patch again, realize it already has the information, and prompt you to log in.
This is from a posting by Ridere a while back.