With external hard drives, Windows often fails to assign a drive letter to it, and no drive letter means it won't appear in the drives window.
Control Panel > Admin Tools > Computer Management > Disk Management
In the bottom-right panel, find the ribbon which relates to your external hard drive. It will have no drive-letter, no name, and will show as "Raw".
Right-click that ribbon and choose "Change Drive Letter & Paths".
Choose a drive-letter.