If he can get some readable display from the computer, when it is running with just the basic background screen, try examining the video display settings, and write them down. Say, 1024 x 768 at 256 colors, or whatever it says. Shut it down and remove the KVM box, reconnecting keyboard, mouse and video cables directly to the computer. Reboot and check those video settings again. Are they the same? Does the picture look just like when the KVM box was in the system?
I'm wondering whether the computer is detecting signals from the KVM box that indicate it is now connected to a lower-capability monitor, causing it to downgrade to lower resolution and color depth all by itself. That can really distort complex signals like movies, etc. If the system without KVM box in place reverts to a different video output setup, just like it used to do before, then you can try to set it manually to the settings it had when the KVM box is in place. Then you can see what those settings do to your display appearance. If it starts to look bad, just like when the KVM box is in the system, then the root of the problem is the altered video display settings. I don't know how you would fix that, but it can point to the origin of the problem. However, if removing the KVM box solves all the problems and you can't reproduce them, maybe the KVM box is the culprit.
My son and I, both with newer LCD displays, use a different approach. The computer video card outputs a digital signal, connected to the display's digital input. The XBox, on the other hand, feeds an analog signal to the display's analog input. At the LCD display, itself, we use the controls to select which input spource is being shown. We're not trying to use the mouse and keyboard as inputs on the XBox.