My WD passport spins, lights up and connects but doesnt show as an available drive My external hard drive fell.  After that I plug it in and it lights up but doesnt blink, the HD spins then stops.  The WD icon in the top right of my screen shows it there as plugged in but it doesnt ever switch to showing data on it. It never shows as an available drive to use.
From your concise description of what happens when you plug it in, the drive mechanism has apparently been damaged - it has happened to me several times. There's not much you can do if there is physical damage. I hope you have a backup of the data on this drive!