Why is my Western Digital Elements SE Portable 500GB Hard Drive not detected on any computer?

I have a  WD Elements SE Portable 500GB (2.5 Inch / USB 2.0) WDBABV5000ABK. When I plug it in, it starts running but no icon pops up on the desktop

Have you checked if the Elements drive is recognized on the Disk management window? You can also try running a DLG test. Check the links below for more information. 

How to access Disk Management in Windows XP, Vista, 7 or 8 to manage hard drives 

How to test a drive for problems using Data Lifeguard Diagnostics for Windows