Ok cid with the data migration info it points toward the driver or a file corruption in FFXIV.
First go to control panel then programs and features. Uninstall AMD/ATI Catalyst drivers. Go to AMD's site download new drivers and install. Test if the game is working correctly again if not.
Uninstall FFXIV and then redownload the game some of the files may have some damage from the data migration from old hard drive to the new.
if you need more help ill make sure to check back every hour or so i just got up for the day.