FIXED!
Tried the reboot tips, plugging in to a PC still a dead tablet. The empty batter shows up then it goes 25%, 50% gold battery fill and then dies. I called Samsung. They were VERY helpful. The lady walked me through a few diagnostic steps. One she had me do was plug into a PC and asked if it recognized the tablet on the PC. The PC did not recognize the tablet. With that step she was fairly certain it was the cable or the Tablet itself. She recommended going to Best Buy (where we bought it) and asking to try one of their chargers. We did that and it went to 25%, 50%, 75%, 100% gold bar on the batter charging icon and repeated (normal charging cycle). So Best Buy just gave us a new cable (we had bought it less than 30 days ago). All is well. The cable we were given is a "rocketfish" so not a Samsung replacement. Samsung was careful to recommend only a Samsung replacement but we'll see. It was definitely a defective cable in our case. Perhaps some of the fixes may just be wiggling a intermittent cable and later a fail (caution on that).
Good luck all!