The first thing I did was an Internet research looking for detail fixes for - Device Manager does not see a DVD/CD-ROM when one is present.
There were a number of text streams that gave accounts of users struggling with the same phenomenon under Win7x, 8x and 10.
And I noticed one curious thing - that other users were also noting that Device Manager did not display a DVD/CD-ROM entry and mostly their statement (no entry in Device Manager) was being ignored in the discussion. Curious. Maybe it doesn't matter?
Also I was unable to find an explanation of what should/would be listed in Device Manager and how the entries actually relate to Hardware.
So edit the registry and edit the Device Manager is the fix.
Registry fix is (under Win10 64 bit) right click the window icon in the lower left corner and select "Command Prompt (Admin)". Then enter this string - (it's probably crucially important to get the characters, quote marks AND the spaces correct, you have been warned

) (I would think and study and rethink what you are about to do first!)
reg.exe add "HKLM\System\CurrentControlSet\Services\atapi\Controller0" /f /v EnumDevice1 /t REG_DWORD /d 0x00000001
Then the Device Manager fix was to select and delete, the last or bottom entry(s) of the Controller list. Then do a restart.
After a looooonnnnng start up Device Manager now displays a DVD/CD-ROM line and it works, I can burn a disk.
Phew

.