
Source: Youtube/John Glasscock
The PS4 is a great console, but its controller has a few well-known problems. Chief among them are the dreaded flashing light bar, and the “blue line of death” that can appear on your controller’s screen.
One of the more confounding issues, though, is when the controller disconnects at seemingly random intervals. For gamers who want to use their own controllers, it can be frustrating to deal with.
A subclass of the PS4 controller not turning on issue is the controller that won't connect to the console. There are several reasons why this might happen, and a few ways to fix it.
Source: Makeuseof.com
Reset Your Controller
First, you have to try resetting your controller. This is a simple process that restores the default factory settings, and should be done first before trying anything else. To do this, press and hold the PS button for 10 seconds, until the DualShock 4 turns off. Then reconnect a USB cable to the controller and the PS4 and turn the PS4 on.
Plug to another USB port
First, try plugging in your DualShock 4 into another USB port on your console. If you're using a PS4 Pro, the USB ports are on the front of the console; on the original PS4, they're on the back.
If you're using a USB hub or extension cable, try plugging it directly into your PC instead. The extra hardware can sometimes cause issues with recognizing your controller's signal.
Got multiple controllers?
If you've got multiple controllers hooked up wirelessly, try unplugging them before turning on your console. This will prevent any issues with wireless interference between all of your controllers.
Check your USB cable
The cable you use to charge your PS4 controller is the same one you can use to connect it with a PC. While it may appear at first glance that the cable is fine, it is still possible that there could be damage to its exterior or interior. Try using a different USB cable if you have one lying around

Source:Businessinsider.com
Check HDR is enabled
If you've got a PS4 Pro and a 4K TV, check if HDR is enabled. HDR mode messes with some things in the system software and might be causing problems with your controller. Turn off HDR mode by going to Settings>Sound and Screen>Video Output Settings>HDR and then change "HDR Output" to "Off." Test out your controller again after doing so
Check Battery
If you've had your PS4 for more than a year, the battery in your Dual Shock 4 controller may not hold a charge as well as it used to. If your controller won't turn on, check to see if it's fully charged by plugging the USB charging cable into the controller and the console.
Check your power button
If resetting your controller didn't solve anything, try checking out your power button for any signs of damage. The plastic piece surrounding this component can get damaged over time, so if you see anything amiss here (or buttons not working), we recommend getting in touch with Sony directly for support or finding a good PS4 controller replacement online.
Update Your Firmware
If that doesn’t fix the problem, you may have to update your firmware. There are two ways to do this: manually or automatically. You can manually download any updates from our website by going to Support > Search for your product > Downloads & FAQs > Select Version Number > Firmware Updates > Download the latest firmware version listed.