How old is your computer?
As Mao just said, it is most likely to be either the hard drive failing or fans. Somehow, I'd say the fans are more likely to be failing than hard drives - but don't take the chance. Back everything up now.. The only real way to determine where the sound is coming from is to open up the side panel of the computer and have a listen. Is it coming from towards the front or the back ... etc.
The error checking functionality within Windows can be an indicator of drive health, but do not take it as absolute. There can be errors without the drive failing (but sound is a dead-giveaway).
Another thing to consider is keeping the computer on as much as you can (ie, copy the entire lot asap without turning your computer off). This is because most of the hard drive wear occurs during start up and shut down, when the drive heads have to suddenly accelerate/decelerate.
Again, I can't iterate this enough - back up everything you have now.
If you're not confident with opening up your computer, or you can't for reasons of warranty, call up the place where you bought it from. I can also come and give you a conclusive diagnosis, but as it would be my company providing the services, it won't be free (that said, I'm happy to make it cheaper for FSN'ers).