RESOLVED - Unable to complete version check - In this instance at least!
OK guys, I hit this issue on a brand new Windows 8.1 install. I tried all the things mentioned in this thread and nothing worked for me, IE Run as Admin, Read-only, reset router, release/renew IP, disable firewall etc
I then started to open some of the files (using Notepad) to check out the contents and these are the 2 important ones I believe.
C:\Games\FINAL FANTASY XIV - A Realm Reborn\boot\ffxivboot.ver
C:\Games\FINAL FANTASY XIV - A Realm Reborn\game\ffxivgame.ver
My ffxivboot.ver was reporting this version number
2014.01.18.0000.0001
However my ffxivgame.ver was blank. I copied the version number and pasted it into ffxivgame.ver and saved it. I then ran up the launcher and my game started downloading a 657mb patch with February dates, so after the 2014.01.18 my version number was reporting. Once it finished download/updating these I could play.
Hope this helps someone, judging from the number of posts there are obviously numerous reasons for this error to pop.