David,
Since it shows up as a STM device when you put it in DFU mode, it means a lot of correct things are happening (good cables, good hardware, nano in dfu mode, etc.).
As happens in some cases that have been reported here before, an incorrect DFU-mode driver gets loaded, and it doesn't work.
In device manager, under the USB controllers section, it should show up as "STM device in DFU mode".
If it has a different title (like "STM Bootloader"), it is probably the wrong driver.
In device manager, select "properties" for the STM device, and look at the driver version. Does it look something like the attached screenshot with driver version 3.0.6.1 from STMicroelectronics?
You can also select the Driver Details button, and it should show the driver file as being STTub30.sys.
The version numbers could be a bit different if you have a different version of DfuseDemo, and that would be ok, but if it is completely different, that is the problem.
If the wrong driver is there, as I suspect, try to manually update the driver, using the "Third Method" procedure on pg 42 (by Fig 72) in the Absolute Beginners Guide. This simply uses the "update driver" button for that device, and navigates to the desired driver file. By the way, when doing so, I found the DfuseDemo driver under another layer of folders for my installation, it was under c:\\Program Files(x86)\\STMicrolectronics\\DfuSe 3.0.6\bin\driver\win10\x64
If that doesn't work, you may have to force-unload the old driver. There is a prior thread in this group (from a long time ago) that details the procedure. You can also send me a direct message and I will try to talk you through it.
Stan
