The Mac would not be able to boot up if it was not able to mount the hard drive with the operating system installed on it. If the issue is as you say and that the Mac can not mount the operating system hard drive then it is most likely a faulty hard drive and would have to be replaced. If the the Mac was able to mount the operating system hard drive and boot up but that hard drive is not appearing on the desktop then that can be changed in Finder Preferences.