Wife's computer is acting up. The Dell Inspiron 2-in 1 would start booting, and then turn off just before Windows 10 starts. I noted that the port for her charger was loose, and there seemed to be issues with the charging. I put in a new port, and just for luck, I got a new battery. That fixed everything until it started the same behavior again. As I was "fixing" it, I put it back together once without plugging in the battery. It happily booted repeatedly with the charger providing power. I plugged in the battery and it was working again. Until it didn't. I decided to get a complete backup, and when I booted, it went into the Dell version of "Repair", and behaved normally. It scanned the hardware and found "Cable issues" and popped a QR code that pointed to a Dell website which gave no help that I could find. I went ahead to try to create a backup, and found that a Macrium boot SD card ran happily, and the backup is running now.
My question: is this really a hardware issue? Is there a reason Macrium, and the repair function would run without problems while windows needs some bit of hardware that is broke? My feeling is that this is software, and possibly the bios getting corrupted. Should I start right off by downloading the latest bios, or should I go to restoring a backup of the Windows partition?   Or....  ?

I am not sure what component would be used by the full Windows version that is not being used by the rescue media doing a backup.  The BIOS (which in the old days provided input/output programs as well as doing booting) is now more of a feature/customization repository.  I am not sure that updating it would do anything unless it were somehow corrupted.  The fact that your system works sometimes, but not other times is not helpful since you would have to do very CONTROLLED experimentation to insure you were only changing ONE thing at a time to isolate when the problem does or does not occur. For example, if using the battery ALWAYS caused a failure but disconnecting the battery never caused a failure - THAT would be significant.  Your information was not consistent so does not really help focus on one issue.  It could be a memory module, it could be something that happens when a component is hot (or cold).  My computer fails intermittently when I turn it on after it sits powered off for a while.  But if I never turn it off (or just power it down and then power up again within a minute) it never fails to start up (note it is 7 years old).  It is probably a component on the motherboard.  But as long as it works reliably for now (there is no need to let it cool off), I will continue to keep current backups and will look for a new computer later this year when DDR5 ram is available.

Hopefully you can get a good backup so the options of a new computer or getting this one repaired are viable.

It was due for a bios update, and, you're right - nothing new.  I switched a couple settings:  Was on Fast boot, minimal checks and I switched to thorough.  Also turned off C-state, as someone elsewhere with a similar problem said it helped him.  I put the battery back in, and booted.  Again, it bombed before windows.  I plugged in the charger and it booted nicely, and stayed on.  I repeated several times, and it does seem reliable now with the charger in.  So,  I think it may be some component that regulates between the battery and charge circuits, or a similar software system.  Still need to do some tests to see if booting with the charger and then pulling the plug allows the battery to take over.   But, she now has a working computer, and just looks at me when I suggest more tests.