To start ensure that each time you connect or disconnect the HDMI ports both TV and connected device are off.
Also ensure that HDMI input is active, as detailed here.
HDMI connectors carry voltage, and connecting the HDMI cable while TV or device is on may easily damage the HDMI port, making it unusable.
The HDMI 3 and Component 3 are separate input. The component input may work, and HDMI port may still be defective.
To test the port do the following:
Disconnect TV power cord, and connected device (eg. Receiver, DVD etc.).
Leave units disconnected for five minutes.
While power is disconnected, test connecting on port three a device that was previously working on HDMI 1. Also use a cable that you know is working.
Connect back power with HDMI cable already connected. If HDMI 3 is still not detected, then the port is defective.
In that case ring Pioneer at the number listed on the owners manual.This model is often advertised as only two HDMI inputs. Call Pioneer to ensure the third port can be enabled.