Here is the final evolution of my Google searches for this issue. This one produces the best links: https://www.google.com/search?q=dell+latitude+e7470+plugged+in+not+charging
Here's the basic debugging chain presented as a funny video: https://www.youtube.com/watch?v=XjB48jGjUVg
The debugging chain offered some hope in that the problem could be in the plug in the laptop, or the cable between the plug and the motherboard. So I got a cable and installed it but sadly this didn't fix the issue.
Here is the cable on Amazon: https://www.amazon.com/Eathtek-Replacement-Latitude-E7270-DC30100VI00/dp/B07HK61LDW/
I accidently lost a lot of my research trail when my browser crashed, but here are a few more links:
This is the mother of all google hits for this problem. It describes the cause of the problem and actually shows a person debugging the issue finding the Dallas Chip in a charger. It also has a link for stand-alone external battery chargers for Dell batteries, which is pretty much my only hope since the problem seems to be on the motherboard rather than the charger so I have to find a way to add charge to the battery for the moments between when I enter and exit the laptop from hibernation mode:
https://www.laptop-junction.com/toast/content/inside-dell-ac-power-adapter-mystery-revealed