When a computer does not turn on after replacing the CPU, it is more likely caused by a short in the motherboard than a bad CPU, but the shorting out of a CPU is possible and should not be ruled out as a cause of the computer not posting. Before removing and throwing away the processor, check a few basic signs that will tell you whether the CPU is bad or not.
Turn on the computer and check to see if all the LED lights come on.
Listen for the processor, case and power supply fans to start.
Listen for the single beep of the BIOS that indicates the motherboard is starting. If you don't hear this beep, the motherboard may not be working.
Look for some type of postcode. This will either be the BIOS entry instructions, the manufacturer's logo or even a flashing cursor. If you get some type of post then your processor is most likely OK.
Connect an external monitor to the computer if the LED lights turn on and the fans start up. No image on the screen is a sign of a bad video card.
Disconnect the power and all other cables from the computer desktop. Turn the computer so the back is facing you. Unfasten the screws from the back of the right side panel with a Phillips screw driver. Slide the panel off the computer.
Lay the computer down and move very close to the motherboard to detect a burnt electrical odour near the processor fan. This odour is unmistakable when a processor burns.
Remove the processor fan by prying out and up the securing tabs. Lift the square processor from underneath the fan and smell it to detect a faint burnt scent. Either strong or faint, this brunt smell indicates a bad CPU.