Open a AMD Warranty ticket and see if they will replace the Wraith Prism. I am assuming it came bundled with the AMD Processor.
If you purchased it separately then see if the Retailer will replace it.
All CPU Fans should start rotating as soon as the Processor receives power, otherwise the computer will shut down from the processor overheating.
NOTE: Upload that video you posted to AMD Warranty to show them what is happening if you purchased the AMD Processor and Prism within 3 years time.
EDIT: Did you check the Power cable to the Prism to make sure it is good and not damaged?
Also when you power up the computer grab the Prism power cable and gently move it around and see if the fan starts immediately or not. If it does then it is either a defective or damaged Prism power cable or it isn't making good contact with the Prism port.
Either way I would still open a AMD Warranty ticket if the Prism came bundled with the processor.
