You can connect a PS4 controller using the micro-USB cable that comes with the device. But connecting a second one requires a different method.
If your PS4 controller won't charge, you can try swapping out the charging cable or checking the charging port.
For those of us who have been around long enough, it's interesting to live in a time of Bluetooth-enabled controllers. Back in the olden days, you bought a new controller for your PlayStation, you ...
How to connect a second ps4 controller to ps4 online, Why Won t My PS4 Controller Connect to the Console How to Fix PS4 online ...