It turns out that the new AppleTV doesn't support HDMI 1.0 cable. I'm much too proud to admit I traveled two hours round trip to the Apple Store to replace the ATV4 so we'll skip right over that part as well as the part about the three tech support reps who had no immediate solution for the TV screen just remaining blank, other than for me to drive two hours round trip to return the device. So instead let me go right to the part where Justin the Senior Tech Rep figured out the problem and restored my faith in Apple and my will to live. The trouble was, as Justin figured out, that the first generation HDMI cable which had worked just fine with that TV and with the previous ATV model, was not up to the standards of the haughty ATV4. Luckily another TV in the house did have a modern 2.0 HDMI cable, and a quick swap was all that was needed. (I'm glad, though, that I didn't accept either the offer to mail back the first ATV and await a new one, or the suggestion to order a $20 USB-A to USB-C adapter--even though the rep said he could mail me a free one, which was very nice even if it wouldn't have helped.) Hope this helps somebody else avoid a long car ride.