Hi,
Not knowing all the details, about the model of display and other hardware involved, my first recommendation would be to either service or replace the display. Then look at the particulars of the connections that were used.
Connecting one display to multiple computers is possible depending on the capabilities of the display and the method used. If the display supports it you can configure the display to recognize one port as a priority, so only one input will be recognized if both are active. Some displays are available that allow multiple active inputs, and use a split screen method, with one half of the display used by one system and the other half for the second input when both are connected and active. It all depends on the capability of the individual hardware.
Then you have the possibility of using hardware like KVM switches, to connect multiple computers to one set of keyboard/mouse and display.
After verifying the hardware's capability, I would also suggest you check out the cables that were used. It is quite possible that one of them could be part of the problem.