I have been playing a ton in the past week. Last time was 7 hours ago. This morning I tried to launch the game as I do multiple times a day and hit my nose on this :

"Unable to complete version check. [30605][20448][10009][10019]"
or
"Version check failed. [...] [30605][10009][10020]"

I have looked online, found and try different options.
  1. I tried disabling both my firewall and anti-virus for the duration of a try.
  2. I tried whitelisting every component of the game.
  3. I tried editing the FFXIV_BOOT.cfg file in note pad by changing "BootVersionCheckMode 0" to "BootVersionCheckMode 1".
  4. I tested my internet connection and tried another one.

When option #3 is on the table, the error message changes sometimes to "A system error has occurred: -2146697211. HTTPS System Error."

During the different tries, I got to the launcher twice. Once every line was changed to a "no connection" line of some sort. And another time I could see the rolling menu with the ads, but the same error pop-up showed up. When these happened I closed the launcher and launched it again to the error message before reaching the launcher.

I am now at lost. I paid a few months for nothing in the past because I could not update the game (a relay tower in a town two hours away was named as the cause by SE before telling me it was my problem). This time I do hope something is possible.