I have a 5 year old Pentium 4 that is starting to make noises. The sound is like a motor revving up then slowing down. If I put my hand on any drive, or on the frame, I can feel it revving up then slowing down. (Does this sound like the power supply, or something I can replace?) Other than that, it works fine. I mainly use it for internet, and burning a lot of disks.
Probably a sleeve-bearing fan, 5 years sounds about right.
Most likely the power supply, for some reason they always seem to go first esp. if it's a noname case-bundled unit. I would pop the hood and try to isolate the noise, temporarily stop one of the fans by forcefully holding the center hub for about 1 second each and see which one it is, replacements are cheap.
At 5 years old even if it is your PSU I'd get a new hard drive at least for back up. There not that expensive and I'd get a larger one that you can always put in an external enclosure if you don't want to install it.