So it only crashes when logging on your machine but works fine on your friend's machine? If so then it sounds like a hardware/software issue rather than an account issue.

Have you tried creating another character and logging in? If it lets you do this then I suspect there's a problem relating to the original character - could be corrupt character settings (Character settings are (by default in Windows) stored in "Documents\My Games\FINAL FANTASY XIV - A Realm Reborn" - if you didn't remove these when reinstalling the game the fresh install may still use them and as a result there could be corrupted data within there causing the issue) or server side related which SE Support would need to investigate though if the character logs on fine on other machines then this is unlikely.

If it happens on all characters then certainly an install issue -again, could be corrupted character settings, antivirus locking a file (ensure you exclude your game directory and character settings from scans), hardware related. Difficult to say without any diagnostic data - FFXIV support will require system information which can be gathered via the options menu in your game launcher.