To properly backup the old Firefox data you need to have another computer run the old hard drive and then use Firefox backup methods to move the data/login/profile onto a usb drive and then from the new Firefox restore them back onto the new Firefox browser. Sync isn't a backup device so that is why you don't the data there. You can't get sync to a non-function device that no longer is connected. At this point if you can't get that drive setup to run and see the data to copy over there's not much that can be done by any users on here. You going to have to take it to a computer shop to figure a solution.