Power off, disconnect battery and hold the power button for 30 sec.

Then try powering up again.

If the same fault shows, is there a pattern to the LED flashing -- i.e., 2 white, 1 amber, etc. ?

I also held down the power button for 30 seconds. That did not provoke any positive change. It is still flashing white after a pause of four seconds.

Sounds like some sort of zombie sleep mode.

A more drastic course of action:

Unplug the system, disconnect the main battery from the system board and remove the coin-cell (reserve) battery for 30 minutes (not seconds).  Then put the reserve battery back in, and try powering up. If the system is in zombie mode, that should wake it.  The reserve battery is located just above the main battery so it's easy to get to on this model.

if it doesn't, it sounds like a bad system board.

Service manual:

https://www.dell.com/support/home/en-us/product-support/product/xps-13-9370-laptop/docs

Thank you, ejn63. The power light flashes white every six seconds.