Have you checked if Disk Management is detecting it? If it is, it may simply need a drive letter manually assigning to it. That's a common problem with external drives, and of course, no drive letter means Windows Explorer cannot show that drive.
So have a look in Control Panel > Admin Tools > Computer Management > Disk Management before dismantling anything!
If it is listed there, right-click it's schematic ribbon and choose "Change Drive Letter & Paths". Then click "New" and choose a letter. Click 'OK'.