Good work on troubleshooting. We will have to check the status of the adapter in BIOS; if the adapter is not detected properly the system will continue to receive power but will not charge the battery. Please follow the steps mentioned below to check if the adapter is detected properly.
Very strange, turned the computer off last night sitting on the desk. This morning I unplugged everything and threw the computer in a bag for a drive to the office. When I arrived and pulled the computer out, it was smoking hot. Got the blinking lights. Eventually it cooled down and seems to be running fine. I never opened the lid when I unplugged everything and bagged it up before leaving. I would have noticed if it was hot when i bagged it up, there was no way not to be able to tell. Will unplugging a USB C docking station activate the computer on battery mode or something? I don't want it to happen again. Again, even if unplugging the docking station would activate the computer, its lid was closed and in a bag. So why the heat? Support assist shows everything is current. The unit is only about 2 or 3 months old. To be specific, what I unplugged from the computer that was turned off at the time: USB C docking station cable AC power adapter External USB SS drive.  
Dell 7760 very hot with 4 amber 1 white blinking