In the attached image i used a trick to make the image on the monitor cast more light on the desk than it appears (big illustration). The scene is lit only with the IDL of the monitor. The small illustration in the upper right shows what is going on: The monitor actually has two display-screens; one that is for the lighting and one that is displaying what is actually visible in the render, almost like a real monitor. The backlight image is connected to the ambient channel (with a value of 5), while at the same time it is covered by a plane that shows the image that should be seen. The plane that covers the backlight has it's property "Visible in ray tracing" turned off, so it does not block the indirect light. Probably the scene would not look right if looked at through a mirror (but on the other hand, a lot of things would not).

 Not directly an answer to your question, but works without too much render setting magic.