I've had this problem a couple of times in the last year, and the following steps fixed my problem each time.
I tried resetting controllers, PS4 database, and all the usual steps people suggest in this thread and others.
If possible, use voice or another controller to turn on the PS4, and power it down completely (not rest mode) Unplug PS4 for 2-3 minutes Plug PS4 back in Attempt to turn on using the controller that wouldn't connect.
It should now work fine
gaming.stackexchange.com/users/164806/user164806
Hold the PS -button and Share -button simultanously for some seconds while the PS4 is turned on.
This will reset all connections of the controller and searches for a new one.
If this doesn't help, try different USB-cables after resetting.
If that also doesnt work, your controller is probably damaged.
gaming.stackexchange.com/users/144899/Otto V.
If you have another controller go in devices > bluetooth and delete all controllers except on with green dot by it and then press ps button and share button on controller that won't connect
it will show up in bluetooth devices
gaming.stackexchange.com/users/152866/Jonathon
I had this same problem.
My best possible answer is shutting down your game and pulling out the power cord from the ps4 and give it a about a half of an hour.
Then you plug it back in then connect your controller with USB and it should be working properly .
gaming.stackexchange.com/users/163638/Ron
The same thing happened to me.
Just turn off your PS4, connect your controller, and then try and turn on the PS4 with the controller after it lights up orange.
gaming.stackexchange.com/users/153609/Al Young
Press and hold the system button for 5 seconds, then press the controller's power button.
Everything should work after that.
gaming.stackexchange.com/users/153715/Norma
Pressing and holding the PS Home button and share button did it for me.
While I had the system in rest mode and charge cable connected.
This was because I had to turn the system on manually and without communication between the pair the system fell asleep Even after pushing the reset button behind the controller.
Then sure enough, they found a connection and the system ran an update.
gaming.stackexchange.com/users/167250/annonymous
I was playing my PS4 two days ago and then packed it up with two controllers that were both connected to this PS4.   I got to where I was going, set everything up and now the controllers won't connect. They show pulsing orange when they plug in, but when I hit the PS Button to connect, it blinks white 1-2 times and goes back to orange.   I have tried resetting them both.  Can anyone help?
PS4 Controller not connecting to PS4 and won't reset?
gaming.stackexchange.com
<controllers><ps4>
gaming.stackexchange.com/questions/263064
gaming.stackexchange.com/users/145341/jdking
If possible, use voice or another controller to turn on the PS4, and power it down completely. You can also hold the PS -button and Share -button simultanously for some seconds while the PS4 is turned on. While there isn't any specific way to surely solve that issue, most people press simultaneously the PS button and the Share button, for few seconds.
The community propose solutions, that might fix the problem.