I don't know where or who you bought it from but you may want to first see if they will take it back and give you your money back.
That being said, this is a super common problem with these. Sometimes it's a power supply problem but not usually. Usually it's caused by faulty solder joints under the APU (the large main chip on the motherboard). This is sometimes fixable but sometimes it's not.
There are a lot of businesses who advertise that they can fix this problem. You can find them by Googling them, you can probably eve find some on ifixit. My business also repairs these.
For you and any future readers who read this, here is a list of things that DO NOT cause this problem:
-HDMI port - The HDMI port has nothing to do with this problem. The HDMI port only affects whether video from the PS4 shows up on the TV.
-Software and updates - These do not affect whether the PS4 turns on or not. Software issues will still let the console power completely on.
-Controller or USB port - Neither of these have anything to do with where the problem is.
-Pretty much anything else...this is caused by a problem with the APU chip...nothing else.
I hope this helps.