Can a computer monitor output light invisible to the human eye?
It depends on what kind of monitor you are talking about. Modern LCD screens use a backlight to produce the light, which is then filtered through the LCD panel. The backlight for most displays is a mini-CCFL, or "cold cathode fluorescent lamps." These can differ in output spectrum, but the do produce a significant amount of infrared radiation outside of human vision. 

For instance, here's a spectrum plot for a flourescent light, like you'd find in an office environment: 



The spectrum for human vision is listed below: