if the CPU fan is not even running at speed, I'd suspect the mainboard, but, naturally you'd want to rule out a PSU or any shorted components/connections that might be loading down the mainboard and/or PSU first...
Remove the GPU entirely, disconnect all SATA data /power cables, and internal USB headers, and drop to a single stick of RAM in required slot...
Retest...if problem remains, try a known good PSU...; if problem remains, your mainboard is the likely 99% chance culprit, as actual CPU failures are VERY rare...
IMPORTANT NOTE: If you do need to try another PSU, use all of the new PSU's modular cables, as modular cables are NOT interchangeable between units....different pinouts at PSU supply connection point!) You can fry all storage and SSD/DVD drives quickly by not observing this!!!