Are any of the wires inside the wire casing broken? This tends to happen to second-hand controllers, especially if the wires where wrapped around the controller to tight during storage.
If the DS4 no longer responds with the PS4 then more than likely it's broadcasting a normal Bluetooth signal. To remedy this, I suggest cracking the controller open and replacing the USB board/ribbon cable. And to answer another persons question as to why you'd just buy the motherboard, the motherboard at $38 is actually cheaper than a new controller, which costs about $65-70 each.
Be careful when heating the panel, if you overheat the panel you can ruin the screen underneath and have to replace it!
What is up with Nintendo and the number 3.5?