|In addition to the above comments I suggest you look in Device manager for the external drive enclosure.|
USB external hard drives are actually 2 devices. First the enclosure and then the hard drive itself. If the enclosure isn't functioning correctly you will never see the hard drive. If the enclosure is functioning but the partition on the hard drive has become corrupted then the drive may not show in My Computer.
Look for the hard drive in Windows Disk Management.