So, if you unplug it, and wait a moment, then plug it back in, the power light does NOT come on?
I would first suspect that the power supply has failed.
Take it to a local Radio Shack and have them try with one of their universal power supplies.
If it works, call WD and see if they’ll replace the power supply (or just buy a new one)
If that doesn’t work, your WD has failed, and you could ask WD to replace it if it’s still under warranty.