[I was writing this as Chas was writing his above, obviously!]
Backup, yes definitely. Cleaning dust out of the machine will help lots though.
Put a new bag in the hoover, find its crevice tool and upholstery brush, and get a clean, reasonably small, long-bristle paintbrush.
Disconnect keyboard, mouse, screen and other connections, but leave the power cord plugged into a mains socket that is switched off at the wall. This keeps the chassis well earthed, as cleaning creates static, which in turn damages sensitive components. You need enough switched-off power cable to be able to move the box around as you clean, so an extension cable might be handy.
Open the case (usually Pozi screws, but very occasionally T10 Torx). Lay the PC on its side so that the circuit board is at the bottom (if it's the old desktop or floor standing style of case). It's worth hoovering the solder side if you can get at it, but not making a special effort if its inaccessible.
Start with the top and clean off all the dust you can see. Brush loose anything that's stubborn. There will probably be three fans: one on the back of the case, one built into the power supply (box on one side with a lot of thick coloured wires coming from it), and one on top of the processor (on top of the circuit board. It has a heatsink with lots of fine fins).
The two that can cause early failure if clogged are the processor one and the power supply. Of these the processor cooling is by far the most important. Carefully and gently dislodge as much dust as you can from the processor heatsink under the fan, but don't dislodge the heatsink itself from the board. If you are confident, you might be able to remove the fan itself from the heatsink (usually self-tapping screws- this helps you to get between the heatsink fins with the paintbrush). If it looks too complex or has bolts or funny clips, don't attempt it*. You might find a cycle of brushing then hoovering, repeated, works best.
Don't attempt to open the power supply box. It still carries high voltages when it's off (higher than mains, usually), and can be a real pig to assemble again later. Just get as much dust out of the grilles as you can easily get to with the brushes you have.
When you've cleared as much dust out as you can, it's done. If keen, you can do the main case fan with meths-soaked cotton buds to wipe the blades. This may make it quieter, but will have little effect on actual cooling performance.
The case and power supply fans' bearings often go noisy. Often they're just bushes, but the better ones have ball-races. Maplins and others sell replacements at a reasonable price, but changing the power supply fan is non-trivial.
If you cleaned it well, you should find the fans' speeds will now stop hunting and settle to a lower pitch, indicating they're having to work less hard to cool the machine. On some machines you can get a processor temperature readout, but the fan speed is a good indication it's clean enough. Expect it to go up in pitch if the machine is working hard - playing video off the internet, making 3D models, or lots of disk access can do it. On mine that's making 360 degree panoramic images, which needs loads of processor power.
You should find once it's clean it settles down again. In a domestic environment, especially if you have pets, it's worth doing once a year as preventative maintenance. I'm doing mine in the next few days.
When we kept parrots, I had a shock one year - I opened the case to find everything covered in fine downy feathers and thus beautifully thermally insulated. Charlie, the hen bird, used to sit on my shoulder whilst I was working (we both enjoyed the company), but she'd preen. You have been warned! ;-)
Hope it sorts it out,
E.
*The processors run so hot there has to be an excellent thermal connection between the processor and the heatsink. This is achieved with a special sticky pad (usually), and it doesn't work well enough if it's ever disturbed. The heatsink is tightly clamped down, and will be fine if cleaned, even quite roughly, but NOT if you disturb the clamps!
