There are no HDMI® devices showing under the External Inputs icon of the Xross Media Bar (XMB™) menu.
HDMI devices are only displayed under the External Inputs icon of the XMB menu if the Control for HDMI option of the TV is set to Off. Change the Control for HDMI option to On to resolve this issue.
NOTE: The Control for HDMI option is available in the Settings/HDMI Settings section of the XMB TV menu.