Well that's the thing. Because you're saying it works completely fine with PC, is very weird. Controller's completely ok there with the same cable, controller and port. There's something not going well with PS4. If it's the controller then should have the same problems with PC as well. Have you tried the obvious stuff like completely shutting down the PS4 and reconnecting/syncing the controller? Maybe through the settings?
Also, what if when that controller was connected to the PC, it did something to it that wouldn't let it connect to anything else but that PC
Do you remember when the issue started? If it started right after connecting it to your PC then there's the culprit. It's all trial and error.