Displays KVM Switch, No working Monitor input

Hello!
About a year ago, the newest monitor for our home's main computer stopped functioning, so it had stopped being used. However, today I was in search of some files I needed that were on our old main computer, so I hooked up the old monitor that came with that computer and it didn't work as well. (The old monitor worked on a different computer). I tried hooking up a few other spare monitors to the old computer, but it they also did not work either. I came to the conclusion that the monitor input had crashed.

So, here's my question: Is it possible to use a KVM switch to display the old computers monitor display on my laptop to get access to my files, even without the old computer's monitor input functioning?