Jsf1973 asked the Laptops forum why his computer was making a very annoying whirring noise.
This is almost certainly a fan--either one that's come loose, or one that's having to work harder than it should to keep your PC cool.
But you shouldn't completely discount the possibility of something far more serious: a hard drive problem. A dying hard drive is more likely to make a clicking noise than a whirring one, but it's best to play safe. Make an extra image backup of your hard drive, just in case. See More on Image Backups if you need details.
Once your hard drive is protected, start looking for a culprit amongst the fans. You need to figure out which fan is causing the problem, see if it, or anything near it, is loose, and clean out any dirt that may cause overheating. How you do this depends on whether you have a laptop (as does Jsf1973) or a desktop.
Shut down, unplug, then open your PC. Then plug it back in, turn it back on, and see if you can find the ultra-noisy fan. If you're not sure, try the Cardboard Tube Test: Get the cardboard tube from an empty paper towel roll. Hold one end to your ear, and point the other to various moving devices in your PC. (If you don't have a paper towel tube handy, improvise. A rolled-up magazine should do.)
Once you find the noisy fan, shut down your PC, unplug it, and examine the fan, what it's attached to, the mounting that attaches it, and anything around it. See if you can find anything that needs to be screwed down. Or if there's something caught inside the fan. In other words, see what you can do to fix the problem.
If you can't find anything, heat may be forcing the fan to work harder than it should, and excess dust could be causing the heat. Heat is also a likely culprit if you don't hear the noise when the case is open. Use a can of compressed air (you can buy them at any computer store) to blow away the dust. Read the safety directions on the can carefully.
The same job is much trickier with a laptop, which unlike a desktop, isn't designed for user repairs. With the PC running, pick up the laptop and hold it close to your ear. Try to determine where the sound is coming from. You might also use the Cardboard Tube Test described in the Desktop section above.
With the PC off, spray compressed air into the vents to remove dust. Use only a moisture-free compressed air canister. I should mention that not everyone thinks this technique is a good idea, since it blows dust back into the laptop. But it disperses the dust and can help.
Don't open a laptop to fix a fan or to clean the insides unless you're very confident about such things. If you decide to give it a try, search the web for instructions (or a video) specific to your particular model. If you can't find such help, or if you're not that confident, take it to a professional.
My thanks to Car54 and mjd420nova for their contributions to the original forum discussion.