Any other way to launch the game than through steam?

[kikix12]

If you install Steam version you actually need to start Steam?!...

You can play it by skipping Steam. Just install the launcher downloadable for the Free Trial from Square Enix and log-in as normal. The launchers are cross-compatible, the incompatibility seems to simply be artificial incompatibility of connecting the expansions with base game, nothing more.

Of course, that may mean you'll have to download the whole game from scratch.

EDIT: Guess I took to long. Anyway, I can confirm this works, at least. That's how I play having used the free trial first.

[lulunami]

Create a shortcut for ffxivboot.exe or ffxivboot64.exe from your FFXIV boot folder in Steam. Launch ffxivboot.

Also if you are getting BSOD from launching Steam, your computer has serious issues (possibly hardware problems like bad RAM).

[Granyala]

Also if you are getting BSOD from launching Steam, your computer has serious issues (possibly hardware problems like bad RAM).

Oh, didn't see that.
I recommend immediate backup of all your data and then I would proceed to reset any overclock to standard do a clean install of Windows, to see whether it is software or hardware based.

If the issue persists, more drastic measures may be applicable.