In the Fallout: New Vegasadd-onOld World Blues, the Courier can say to their brain: "Once you're back in my head, I'll watch television. Lots and lots of television", implying that there are working television sets.
Intact television sets in Fallout 4 will display the message "Please Stand By", if powered.
Certain television sets in Fallout 4 have an eerie reflection to them when not powered, in Sanctuary Hills specifically. The reflections, while sometimes similar to the surrounding area, appear to be of entirely different locations altogether.