All PCs have had & supported plain old 640x480 VGA standard connectors and modes for ~15 years, so you're pretty safe that any display you connect will work well enough in safe mode to get what you need done. Just borrow a display from one of your other boxes.
FWIW many "brand name" PCs (Dell/Gateway/HP) actually have built in restore capability on the HDD. look around and see if there's a hidden folder or partition that might contain the XP installer or a custom restore scheme.
Personally, this is the point where I tend to remove the HDD from the older machines stuck it in a USB enclosure and copy/wipe off all the data that way.
Good to hear about the display. I think I might be able to borrow the missing cable from one of my computer teachers.
The six year old Gateway died about three years ago, and the Geek Squad didn't save anything and just put XP on. I have not idea what is and is not on there, but I remember reinstalling Office because the version that came on it was gone.
The Gateway is an all-in-one, and I don't want to brick it. The headless Dell in the basement obviously isn't, but I'm still not confident enough to open something that isn't a Mac.
I guess just getting a jump disk would be easiest. Perhaps I'll get one today.