I tried that, but when the launcher started up it still began to download FFXIV.

I realized this may be a problem with the version checks, seeing as there are two of them, one from a more recent date while the other was before my laptop crashed. The recent one thinks I don't have FFXIV while I presume that the other one does. I would say the problem has been fixed, but the launcher isn't able to read the older version check for some reason.