Looking at similar issues, I have deleted any and all system files for FFXIV left on my PC after uninstalling it, and also moved the game from my USB stick (drive G) to the main hard disk (C).
I do not know which of these did it, but the game works as it used to now. It worked fine before and after migrating it to the jump drive for some time, so I doubt that was it, but I'm keeping it on the C drive just in case!