My friend has the same problem, you can "quick fix" it by deleting the "FFXIV_BOOT.cfg" files in "Documents/My Games/FFXIV" with the launcher closed, then starting it again, then you'll have a "fresh" launcher and can connect, but once she did, she tried closing it and opening again and the problem was back... for those who really need to connect while waiting for the square enix launcher fix, i guess it's a problem on their side or idk why so many ppl would randomly have this issue out of nowhere the same day anywhere in the world