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