It's most likely that your computer screen's mapping isn't the entire "map", it's only a section, with other things on the map as well.

In that case, you're going to have to scale the image texture down, UNcheck Tile Image, and use the X-Y Coordinates to move the scaled image into the correct position.

IMO this is the hard way to do it. If I was doing something like that, I'd take the monitor OBJ into Wings 3D, and remap the screen to take up the entire map, and have it as it's on material group.

                                                                                                                    

Poser 10

Octane Render

Wings 3D