Does a TV unplugged radiate?

As long as it is unplugged, there is no radiation because radiation is produced by electric waves. Since it is electric waves, it is only when it is energized.

Common sources of electromagnetic radiation : In general, radar systems, television, cell phone and radio transmission systems, radio frequency induction and media heating equipment, radio frequency and microwave medical equipment, a variety of electroprocessing equipment, communications transmission stations, satellite earth communication stations, large electric power generating stations, power transmission and substation equipment, high-voltage and ultra-high-voltage transmission lines, subway trains and electrical trains, and most household appliances are can produce various forms, different frequencies, different intensity of electromagnetic radiation sources.