First and foremost, have you tried resetting the controller?
If yes, the board to which the USB plug is attached is also readily available on eBay, so you could try swapping that as a last resort. But before, there's something else you might want to give a shot at.
I actually recently had a Dualshock 3 that exhibited a behavior very similar to your Dualshock 4; i.e no response at all even when plugged directly into the console, and inability to charge no matter what cable/charger I'd use.
Opening it up, it turned out a couple of vias on the conductive film that lies on top of the motherboard were damaged (for whatever the fuck reason). Simply replacing the film revived the controller.
The part I'm talking about is the one that you can see in "Step 7" of the following guide:
https://www.ifixit.com/Guide/DualShock+4+Touch+Pad+Replacement/22684
That "thing with the green lines", which looks like this in real life:
https://www.google.co.jp/search?q=d...ved=0CAYQ_AUoAWoVChMI-u-jnrXoyAIVhxuUCh1mDQpM
Replacing it should be easy enough, although if you've never done anything similar in your life, I'd advise to ask a friend with at least a little bit of experience. The entire process should take somewhere between 10 and 30 minutes.
Conductive films for Dualshock 4 are easy to come by, and very cheap (1 or 2 USD), so I'd say it's at least worth a shot if you feel comfortable enough doing it.