The fan on top of your cpu heatsink does not run at all?
assuming the fan itself is not broken, can you power it off the psu? (You'll need an adaptor to do this and the fan will run constantly at 100%)
I think you have major motherboard problems if its not telling the cpu fan to spin up
I had a motherboard which did not spin up the fan until it saw some heat from the cpu. Itt made boot time fun because the 'cpu fan fail" alarm would go off for a several seconds until the fan started spinning. LOL
Disabling fan control and leaving it set to max was the simple fix. This was an asus mobo for what its worth.