If you are admin, then you would not need to unlock/unsecure that folder. If you are not the admin, login to the admin and right click the SquareEnix folder and go to the security area, and add everybody and mark for full access. Then go back into your normal user.

If you are an admin already, then it as stated above, anti-virus or anti-malware or firewall program could be holding it up. I know each time the patcher changes I have to confirm my anti-virus program to allow it to load up. I would say add the EXE's from the SquareEnix folder to the exception list in your program. That should do it. Some programs are better with games than others.

End all - uninstall the game and redo the installer program that redoes the patcher and then relaunch the patcher. That is if you were able to run the game already in P4, it's the same client with a patched patcher. You would have to redownload the game, but it most likely would clear your issue of an uninstall/reinstall.