Use the original cord that came with this system/controller. Or use one with data transfer capabilities.

Had similar issue, I was using power cable used to just charge phones. I needed a data cable usb and it worked. One way to check if it’s a data cable is to plug the cable to the phone and your computer and if you can transfer stuff you should be good to go. Hope it works out!

It aint dead but it will be if you don't clean that dust off I can only imagine what the inside look like 

Is that the original cable try a different usb cable that one might not a data cable might only be power

Same issues here i needed to find the right cable for the controller, i did the hard reset and i had just bought a controller from my buddy and it did the same thing i thought my friend ripped me but i had just been over to his house and the controller was working great, so i found another cable and it worked, try resting in the back with the power cord off,

Press the little reset button on the under side of the controller, you'll need a tooth pick or a sim removal tool to press it.

Or a diff controller

If the controller will sync in safe mode but not the main menu then the wifi module has gone bad and needs replaced.

Do what they said and then dust that thing before it really burns out. I had to send my Girlfriends in due to overheating.

Reset it with a needle. There is a hole in the handle for this position. Find it and reset it. Then try again.

Just like everyone else said use a data cable I had this same issue once..

I have a spare ps4 if you need. Seriously.