What specific parts of a radio receiver use power? Does receiving the signal need the battery
You can receive a signal without a battery, but it has to be strong enough to drive whatever output device you have. It would take a VERY strong signal to drive an LED, not so much to move a very sensitive meter, and even less to be audible in a sensitive headphone. If course to be audible it has to be demodulated. So the crystal receiver that has been a kid's first electronic project since the 1920's: an LC circuit to tune a long-wire antenna, a crystal diode to demodulate, and a high impedance headset to listen. AM only. RFID tags use the same principle but they actually create a modulated field load to the transmitting antenna to "answer" the reader. They depend on a very-low-power IC that can take the received power and reflect it back to the antenna with the ID as modulation. That's the limit of my knowledge, there may be RFID's that retransmit on a different frequency.