This is a battery contact problem. See video.
UPDATE: Packaging and shipping cost over $40. Frustrating for a $250 computer. It turned around in about 10 days and the repair was free. Seems to be in good working order now.
Factory reset was step one of Asus troubleshooting, and was a waste of time. I had already done my own troubleshooting.
When running on battery, when you pick it up from the near left corner, it shuts off. If it doesn't go back on by itself, then pick it up from the front right corner and it will restore.
On power cable, when you pick it up from the near left corner, the battery/charging icon disappears.
I conclude that there is a problem with the battery contacts. My unit is under warranty, so I am not going to try to open it up myself. Sending it in for official repair. Will update with outcome.
Asus tech support in USA 1-877-339-2787.
Asus tech support in USA 1-877-339-2787.
UPDATE: Packaging and shipping cost over $40. Frustrating for a $250 computer. It turned around in about 10 days and the repair was free. Seems to be in good working order now.