Make sure Internet Explorer is current (through Windows Update). Also make sure both .Net 3.5 and 4.x are up to date there as well. May have to enable the v3.5 by opening the add/remove programs control panel (appwiz.cpl from search/run box) and clicking the link for turning Windows features on/off--depending on which flavor of Windows you have, it may be listed under a Legacy heading.

Make sure TLS support is enabled for the internet properties at the operating system level (run inetcpl.cpl from your search/run box, go to the advanced tab and scroll down to the section about encryption).

Make sure your security isn't blocking the game's executables from internet access (there's about 6 of them in two different folders..ffxivlauncher, ffxivboot, ffxivupdater, etc). We have seen things get blocked by firewalls, antivirus, Windows Defender/Essentials, etc. in the past.