I have a Gateway, not sure what exact model, it's from 2003.

Anyways, late last night while I was away from the computer, it suddenly started making a really loud whirring NOISE. I immediately ran in an cut the power, fearing it was on fire or something. After removing the cover and seeing nothing really out of the ordinary, I turned it BACK on, but it made the loud noise again.

Then, when I turned it on today, the noise was gone.

From what I have concluded, the noise appears to be coming from this box.

http://i9.photobucket.com/albums/a63/funkydunkleman/000_0252-1.jpg

Now I have almost no knowledge of Computer HARDWARE whatsoever. Most of my knowledge is of software.

So can anyone give me any help here?

What is that box? What does it do? Can it be fixed?
Replaced? Manually? Cost?

Any help would be greatly appreciated. Thanks.Welcome to the forums.
That box looks to be your processor cooler.
The noise would be the fan either spinning very FAST, or failing.
I advise you follow the steps here to clean out your computer, and SEE if that helps.
If not, you will need to replace the fan on your heatsink, or replace the assembly (either way, shouldn't be too expensive or difficult).
Hope this helps.I actually just cleaned out my computer, Thursday I believe.

The fan is currently working just fine now though. It's been on for about 70 minutes.

Hopefully it was an anomaly.Good to know it's now working, it may have been a temporary glitch.
If it continues, best to replace the fan I think.