Cannot create Recovery USB

You can also make a recovery flash drive using the Microsoft Media Creation Tool.

https://support.microsoft.com/en-us/windows/create-installation-media-for-windows-99a58364-8c02-206f-aa6f-40c3b507420d

If you haven't already, and the system has a spinning hard drive, run a full diagnostic on the drive as well - F12 at powerup.

The broken system is across town and I'm trying to prepare everything I'll need while I'm on my own system.  I have the Dell Service Tag for the broken system, but I don't have its Windows product key (if that should be needed). Its drive works well enough to get it into the system diagnostics like System Restore, but as I said it's only got 2 checkpoints saved and they are both unusable.

What model Optiplex are we working with?  Version of Windows?  What type of drive is being used as the boot drive?

Sounds like you may have gotten a virus.  I'd replace the boot drive and start over.

On a working PC, you will be downloading Win10 to an 8GB or bigger blank flash drive formatted to FAT32. They often come formatted that way anyway.  Download Windows 10 Disc Image (ISO File) Microsoft site  Download the ISO. It will be in your Downloads folder. With flash drive inserted, click on the ISO and follow onscreen instructions Win10 will then be loaded on the flash drive. Takes a little while. When ready to load Win10 from flash drive, boot from from flash drive on your PC to load Win10. Make sure BIOS is set to AHCI and Secure Boot on.

When a window pops up asking what partition to load Win10 on, delete all previous partitions except for System and MSR if reusing a boot drive. Then click on Next or Install. Win10 will then automatically create the appropriate partitions and load. If a window pops up asking for product key, click on link that says "I do not have a product key." Win10 will then continue to install using the product key that's embedded in BIOS. You'll still need to activate it online.

Do this if  by chance ejn63's suggestion doesn't work.

In case of 2 or more drives, like with 1 or more used as storage, make sure only the boot drive is plugged in during load.

This is a Optiplex 5040 with 8 GB RAM and 250GB disk running Windows 10.  I found no obvious issues with the hardware, chkdsk said the disk was ok, etc.  But the restore points were useless and none of the Windows repair tools could fix the registry.  I installed Win 10 22H2 from a flash drive which took about 2 hours to install, plus more for Windows Updates, plus more for installing Dell's Support Assist which updated even more stuff.  The system is back up and running.  I have no idea how the registry got corrupted, in over 25 years using Windows that's the first time it's ever happened to me.

I was disappointed that Dell's OS Recovery Tool is broken somehow.  

I'm glad you got it working and am surprised to see it took about 2 hours for Win10 22H2.

Last year, I did 2 Windows 22H2 installs on SSD's that took about 10-15 min from flash drive.  There's aspects of Win10 that can be painfully slow on an HDD, like restarts and updates.

I have this problem too.  I found the solution in another thread.

Please try the steps given below :-

In the search bar, type: command then right click cmd.exe on the menu and select "Run as Administrator". This will open a command prompt window.

Type the command: cd C:\Recovery\OEM then press the Enter key.

Type the command: del install*.* then press the Enter key. (Dont include the asterisk symbol which means after install give a space type . (dot)

Press the "Y" key then press the Enter Key.

Type the command: EXIT and then press the Enter key. (This will close the command prompt window.)

Thank you to HarpalSingh69!!