XPS 13 7390 2 in 1 replacement battery

To work what way? You can't turn the laptop on or off?

@demonru​ Fair question. The first two non-Dell batteries that i bought were not "recognized" by my XPS 13. The Dell battery was recognized immediately.  I can still turn on the laptop by simply raising the cover, but, yes, i have not solved the power switch issue. I could buy a new power switch, but i am not convinced that it is a hardware (and not a software) problem. That is why i am asking the community if anyone else has had the same problem, and how they resolved it.

Ok, I see, let me rephrase. Can you describe the power button behavior? How did you find that it doesn't work? The steps you did?
I need every single step like: I open the lid, it turns on, loading Windows, I see my desktop, I press the power button - nothing happens! Is it like that?

@demonru​ Unfortunately, your description is precisely correct. Pressing the power button does not do anything at any time.  It is as if it is disconnected, but I checked and confirmed that the ribbon cable is properly connected.  As an example, I cannot do a forced shutdown by holding down the power button.  Nothing happens; fortunately, I am able to completely start up the laptop by simply lifting the lid. 

It may be important to note (or not) that I had a repair person work on a separate problem (one of the fans stopped working) recently. Strangely enough, the inoperative fan is now working fine, and I no longer get an error message when I start up or when I run the Dell Support Assist program that checks all of the hardware. I also replaced the battery, but that did not fix the inoperative power button. The power button worked fine before the repair person tried to fix the fan.

Thanks in advance for any ideas you may have.

The autopsy will tell :)
https://www.youtube.com/watch?v=QbRmJP4WO6E 
but honestly so many things could be involved, like the ribbon cable is properly connected, but it might be broken inside. I don't think there's a way to troubleshoot it remotely. ;(

Problem solved!

I opened the case and found that the tiny ribbon cable between the power button and the motherboard was not securely attached.

Plugged it in and now all is well!

Thanks for your time and interest in helping me resolve this!