Chosen Solution
My PS4 Pro does not turn on any more. The blue light flashes and it beeps, but fan doesn’t turn on. If you do this again nothing happens anymore. I first have to disconnect and connect the power cord, then the blue light and beep sounds is coming again. Now I read a Q&A on the PS4 when people hit the box or dropped it from 2 inches and then it worked again, this does not work for me. Is it likely that the power supply is damaged? I would suppose, that if the power supply would be okay, at least the fan would start rotating.
If i understand you correctly the PS4 itself turns on but not the fan? If power supply is damaged you wouldn’t get any lights or sounds at all. Unfortunately it’s a common problem on the PS4 pro that the fan stops working. Usually replacing the fan will make it work again.