It may just need a drive letter assigning to it manually, as Windows sometimes fails to do that automatically when you plug in an external hard drive.
Go to Control Panel > Admin Tools > Computer Management > Disk Management
In the bottom-right panel, find the ribbon that relates to your Passport drive (it will have no drive-letter and may be described as "Raw").
Right-click that ribbon and choose "Change Drive Letter and Paths"
Choose a drive letter from the drop-down box.
Click 'OK' and wait for the ribbon to update itself.
The name of your Passport drive should then appear on the ribbon.
You should now be able to see it's icon and name in your computer drives window.