Why am I getting signs of high RF radiation, while the desktop computer turns off?
As long as your desktop PC is plugged into AC outlet, the internal power supply (PSU) is in standby mode providing +5VSB standby power to mainboard, so the computer can wake up from power buttons and/or keyboard and mouse resume signals. This +5VSB voltage is always on. 

To produce this voltage, the PSU must be operating, and therefore continuously switching at primary amplitudes of 200V-300V (DC rectified from AC mains). PSU switching generates noise on all rails and return grounds, switching amplitudes of this scale are difficult to contain. More, when in standby mode, the consumed power is much smaller than the nominal power, so at low load the PSU switchers and inductors/transformers usually operate under very unfavorable conditions, and ripples and ringing from PSU switchers can be even higher than under normal operations. As result, this "noise" propagates along every conductor, including shields of cables that connect mice and keyboards, which acts as antennas.

The same happens in LCD monitor, its PSU is still in standby mode, and still switching and emitting noise.