External Hard drive...is it dead?

I went to go back up some very needing-to-be-backed-up files today and lo and behold, my external hard drive did not show up on my desktop or in finder. I tried it on my PC laptop, and it's not showing up there either. The little green light is on, although it's not making many noises. Then again I don't think it ever really has...I've tried turning it on and off, restarting my computer, trying it in a different USB port, and making sure everything was properly plugged in. The hard drive is a Maxtor brand hard drive...probably almost 2 years old at this point in time. I rarely keep it plugged into my laptop by USB unless I'm using it, but it's always connected to an outlet. It is not showing up at all in my disk utilities. I think I have only connected it to my mac once or twice (my macbook itself is just a few months old). In the past I've always had a PC...so I definitely have no idea what I am working with here.
Do you think maybe just the USB cord is dead? Or is the whole hard drive dead? If so...is there any way I can save the files on it?

Is this an AC powered external hard drive? In other words, not bus powered?

It may have completely failed or it might be an electronic failure. If the electronics on the drive is what failed, it may be possible to remove it from the Maxtor case and place it in an external carrier. However, if it's AC powered, that's not going to work. You would need a self powered adapter instead.

Yes...it's AC powered? By that you mean it has a separate cord and plug that goes into the wall, right?
...so does that mean it has failed?

I'm sorry, you'll have to speak really low to me. I'm not an electronics person.