A CPU fan is installed inside a computer to creates airflow and draw heat away from the computer's processor. Several symptoms may indicate a broken or malfunctioning CPU fan. If the fan is broken, it should be replaced immediately.
If the computer begins making more noise than usual, it may mean the CPU fan is clogged with dust or wearing out.
If your computer starts running very slow inexplicably, it could mean that the CPU fan is not functioning properly. When a CPU gets hot due to a bad fan, the computer will run much slower.
If your computer experiences crashing, it is a possible sign of processor overheating and a broken fan. Motherboards are designed to shut off if the processor reaches a certain temperature to avoid permanent damage.
Even if your computer is not slowing down or crashing yet, if the CPU temp is high, it may indicate the fan is not working properly. You can check CPU temp in the BIOS setup utility upon start up.
The easiest way to tell if a fan is broken is to open the computer's case with a screwdriver and see whether it spin when the computer is turned on. If the fan does not move despite being plugged in properly, it is broken.