you were right to check the mA.
however if the device powers up and you hear the drive spinning, then it is a OS problem.
to eliminate any doubts on the drive, check it on another pc and see what it does. it will most likely work just fine...
to see if the OS is the problem, if you run Windows, do try to put Ubuntu Linux via wubi (http://wubi-installer.org/) as a test on your machine.
no need to put new partitions etc.
see how that plays out with your WD drive. you can also run the ubuntu directly from a usb stick.
if windows is the problem, then try to plug your drive via a usb hub (if you have one at hand) or a shorter USB cable (if you do not already use the one of the drive...).
also do some spring cleaning in the registry (http://www.piriform.com/ccleaner)
and update windows and drivers.
it might also help to remove hardware from the device manager (like the USB controllers and stuff from your mainboard), restart, allow redetection, restart and then plug the drive again.
weird things happen with windows sometimes.
pluging in a new usb device (i.e. camera) and afterwards your hdd might also trigger a correct recognition from windows...