it could be a fan dying - take the cover off and listen for where the noise is coming from. If it is the one over the processor do not let it die either change it yourself or get someone to do it for you.
This job does not require you to touch any part of the works.
Find, beg or borrow, the most powerful Hair Drier that you can and fit it with a reducing nozzle. Turn it to run on cold and check it out, on your hand.
Turn the PC off and unplug it > Touch a radiator, or similar, to remove any Static Electrical Charge you may have > Take the cover off the PC > Direct the Hair Dryer's air blast at any fans that you can see. There is no need to touch them.
At the Rear-Top,usually, is the PSU (Power Supply Unit). Try to blow this in both directions.
Give the rest of the case a blow to remove any accumulated fluff and put the cover back on.
With any luck the problem will be considerably reduced.
Hi dp600. The way to be absolutely sure where the noise is coming from is to remove the case cover. then get a sheet of A4 paper rolled up into a long tube about 25mm diameter and use that tupe with one end to your ear to locate the noise source.
The noise is almost certainly the processor fan bearing. The fan is part of the heatsink assembly. You haven't told us anything about your computer, but most computers over the past few years use a heatsink the clamps down on the processor by clips that locate on the processor socket. Replacing the heatsink assembly is not difficult but must be done carefully. What is much safer and easier is to buy a heatsink that has the same size fan, remove the fans from both heatsinks - a simple matter of undoing 4 screws - and fitting the new fan on the old heatsink. This way you don't disturb the thermal contact between the heatsink and the processor.