|I'm assuming the processor is not already damaged from overheating....|
(e.g. if the mboard shut down automatically when the processor overheated it's probably not damaged.)
(cpu in this = the processor, or microprocessor - the computer case the components are in IS NOT A CPU ! )
Unplug the case/power supply, or switch off the AC power to it otherwise.
Power off your monitor.
Open up the case by removing the left panel as seen when you're looking at the front of the case.
If the cpu fan/heatsink has mung (dust, lint, etc.) on it, clean it off, but DO NOT use a vaccuum cleaner to do that (they produce a tremendous amount of static electricity when running, and anything connected to them can discharge that to your components) - use canned air, or an air nozzle if you have access to an air compressor, or an artist's brush that can be used in small spaces, etc. It may be difficult to clean the top of the heatsink under the cpu fan - the most likely place to have mung on it - and the bottom side of the cpu fan blades unless you remove the fan. If you have a case fan, clean that too if it needs it.
Also check for mung on the video card fan and heatsink if it has that, and the power supply's openings / fan.
With the cover still off, restore the AC power, start the computer and make sure the cpu fan spins - if it doesn't spin, if you're sure the power supply is working okay, don't use the computer until you have replaced it.
If it spins too slowly, and/or if it makes rattling or screeching noises, most likely to be noticed when the computer has cooled to room temp, has not been used for a while, and then is started up, the cpu fan's bearings are failing - the cpu is likely to overheat as a result of that if it can no longer spin it's full speed - replace it as soon as you can.
I'm assuming no one has been fiddling with the processor's heat sink since the processor / computer last worked properly. The clamps or clips for the heat sink must be holding down the heat sink so it is NOT loose ontop of the processor in it's socket.
The three (or four) pin hole female wiring connector from the 3 (or 4) wire cpu fan must be connected to the 3 pin header for the cpu fan on the mboard, otherwise, many mboards will shut down automatically a short time after you boot when no rpm is detected from that header by the mboard's bios.
The same thing will happen with those mboards that do that if the cpu fan no longer spins that connects to that header, or if it spins slower than the bios allows for a minimum rpm.