The screen on my XPS all-in-one (MS Windows 10) is out of action. Local repair shops no longer have the parts to fix it. I have no spare monitor to connect to it, and am looking at options. If I replaced it with another all-in-one [which is what I am inclined to do], would I be able to slave the new PC [use it merely as a monitor] to the old one initially, use some key combo to switch video output to it, so I can log on and extract my files? Or is the only option [other than buying a monitor which I would then have no further use for] to remove the hard disk?
No you cannot do that. Just buy a new computer. Use your backups to replace your files. Copies, system image, backups can be used. If none are available, remove the hard drive and use an inexpensive enclosure to retrieve your files.