How To Fix Ps 4 Controller Turning On By Itself. Use a small, unfolded paper clip (or something similar) to press and hold the reset button for at least five seconds. Connect the controller to the console with a USB cable, and press the PS button.
DualShock is a line of gamepads that was developed for PlayStation systems. Hit the PS Button on the controller to hopefully turn on and pair your controller in one process. Sounds like either a problem with the circuitry (probably not repairable but more likely), something stuck under the home button in the controller housing itself that's constantly holding down that button (probably repairable but unlikely), or the button is sticky or stuck on an edge making it not release (again, probably repairable but either.
Based on your description, your issue is that the wired controller will randomly turn off.
How to turn off and charge the controller.
However I can bring up a few possibilities here: Your PS button is not seated properly. Turn your controller around and look for a small hole on the back of the controller. Hit the PS Button on the controller to hopefully turn on and pair your controller in one process.