This is an extra safety feature that dell uses in case a fan does fail the user will see the failure and avoid potential harm to the pc cpu.
Cpu fan failure dell inspiron.
Next is a reputable local repair shop that charges by time not by the job.
Locations that charge a flat rate for the job.
Least expensive way is to replace the fan yourself.
Processor fan failed to respond correctly try blowing out the vents with canned air.
The fan you need will depend on your graphics type integrated or amd.
Most expensive will be dell or geek squad etc.
Inspiron 5559 out of warranty cpu fan failure.
If the fan is not working then i have to assume the system is shutting down as the cpu will overheat.
Lint and dust accumulation prevents air from flowing around the cooling fins and causes the fan to work harder.
Assuming you have the original dell fan it would appear the electronics in the fan have failed even though the fan is working.