error 4013 keeps popping up when trying to restore old iPad

I was going to give this old iPad (3rd generation, 64 GB Wi-Fi = Cellular) of mine to my niece, and followed all of these instructions on this link https://support.apple.com/en-us/HT201351. But it turns out, she still couldn't turn it up or use it. It kept going in this vicious circle of turning up the "Hello" page, asking for the language, country, network, etc. Then screen would say unable to activate. So I forced it to restart, apple log appeared, then the black screen that showed "connect cable to iTunes" appeared. So i connected it to my Mac. My Macbook is very new <6 months old with El Capitan OS X, iTunes is also updated. then followed these instructions on https://support.apple.com/en-us/HT201412 (I followed item #3). I chose "update" first, then when this did not solve my problem, repeated the steps and chose "restore" instead. At the end, still no resolution, window that says error 4013 has occurred. This old iPad, of course, is already past its Apple Care warranty. I am surprised to find that many people has this same issue, and no announcement of a product recall on these things. I have the original iPad (first generation), and thank God, it's still in working order, being used by another 2 year old niece. And the irony is this 3rd generation one has problems. Is there any hope that this can be fixed. I paid top dollar for this piece of technology, I bought each and every iPad and iPhone model, even macbook airs/pro, macbook there is. And this is the one that gave me the worst problem, it seems a waste of big money. Should I just take it in for repair (and pay the service charge)? If anyone can share what solution they found for the same issue, I would be grateful. Thanks