As others have suggested, the only option I can think of is Tinycore but you’ll need to get the Microcore version (aka Core ISO with no GUI). This should run on 32MB RAM but leaves you very little headroom with a very barebones install, and obviously no GUI of any kind. [Source]
I looked up the Compaq Armada 1700 and saw that it came with 32MB soldered with one slot available to expand up to 160MB. It’s a long shot, but if you can find a working 32MB, 64MB or 128MB memory module for this you should be able to run TinyCore with a GUI. Adding more RAM would also open up options like Slackware.
It’s not clear to me if Debian will work or not, even with maxing out the RAM in this computer. There is a low memory install mode you could try but I think even that requires at least 256MB which is beyond the theoretical maximum this computer supports.
If all you want to do is prove to yourself that you can install Linux on this computer then Microcore might be worth a try. If you want a usable system with a GUI then you’re probably going to have to add more RAM.
This could be a long shot, but so long as you do NOT connect it to the internet, you could try sourcing a Linux distribution from back when this computer was released, I’m thinking Redhat Linux (before RHEL and Fedora was a thing) or Debian a very old version of Debian. However even if you do succeed in this it’s probably not going to be usable.
Good luck!
It might sound ridiculous but I switched to Linux to take ownership of the things I own.
The lesson for me was Windows Genuine Advantage in Windows Vista throwing a fit whenever I wanted to make a change to MY computer. In this moment I realized that so long as Microsoft was in my life, I will never truly own the hardware I purchased, the system I built with my own two hands. I was late-teens at the time working a dirty minimum wage job, so this was big to me.
This is a lesson I’ve carried with me the rest of my life and colours all purchasing decisions I make. I’m not giving up my hard earned money if I don’t actually own the product I’m purchasing.