I appreciate it's a bit late now, but don't ever verify files through Steam for this game. It does sound like a reasonable thing to do, but that only works for games that update via Steam. This game (and some others) gets the updates itself through the launcher so you can't use the verify function as the files Steam have aren't the most up to date version (Steam only has 2.1!)

So basically when you verified files, it compared the files on the disk (3.45) to the version in Steam (2.1) and it realised they were different so set about putting you back to 2.1. And then when that had finished the launcher would then redownload all the files to put it back to 3.45. When you did the second verify it again reverted back to 2.1.

Regarding the actual game problem though there's a few things you can try. For the script errors, open Internet Explorer (even if that's not your usual browser) and go into the options and delete browsing cache files, specifically "Temporary Internet files and website files". The launcher is actually piggybacking off of Inernet Explorer so that's why you have to clear the files for that browser even if it's not your normal one.

If you're still crashing, try going into your Documents folder and look for a "My Games" folder. Inside that will be a folder called "FINAL FANTASY XIV - A Realm Reborn" which actually has all your hotbar, macro, UI settings, etc. Rename that directory to something else (temporarily!) and then try and open the game again (it'll recreate that folder and ask you the basic questions like if you have an account already etc).

If that version works then you can try moving the files inside the directory back in until you find the problem one(s). To speed things up, inside the directory are folders starting FFXIV_CHR which are your character data (macro, hotbars etc) so you can move those folders back for all your settings per character (the character itself is stored on SE servers, this is just your local configuration files).

Hope this is some help!