Okay guys, I need to start over. Turns out the noise is NOT coming from the hard drive. In fact, it is coming from some part of the lower section of the motherboard. The motherboard is an ASUS P5B-Plus. It is not any of the fans and I doubt it is the graphics card, as it is brand new.
I've taken a video so you can hear what I am hearing. I replayed the video to myself and it is difficult to hear, but the noise is there.
Here's the video:
Strange motherboard noise - not from the hard drive or fans - YouTube