It might be suffering stiction, where the grease in the motor bearings freezes up and prevents the platter(s) from spinning.

One possible fix would be to apply power, and give it a sharp whack with your hand or a screwdriver handle (be careful not to dent the cover, or more serious damage may occur). Another, more risky method, is where you can actually remove the cover to expose the inner mechanism. From there, you can then spin the platter manually (don't touch the platter under any circumstances!! Only touch the inner hub). Ideally, you should do this in a dust free environment, but if you're careful, it'll get it working long enough for you to get your files backed up (never trust a drive that's been opened up like that for important stuff, unless you back it up vigilantly).

Good luck!

c