I had this problem today, i was in a trip and i had to get my power and hdmi cable there cause my friend had the ps4 and forgotten the cables. So i returned and just plugged my ps4 to power as it was before. The ps4 did not turned on at all then i had realized that the power cable (the original cable in the ps4 box when you buy it) is a little loose at the connection point to the console so you have to push it hard and it will just connect (my ps4 is region 2 so the cable is not the fancy region one cable that is made just for ps4 and its a little kind of bad cable. While playing my friend had this problem too its not just when you disconnect it from the power supply
I hope this help you guys