some tvs have hdmi but it is not for video. has something to do with diagnostics. I have one like that. what is the full model number of your tv.
I connected my computer to HDMI port 1 on my JVC TV. The computer sees the tv as a second monitor but when I try to select the HDMI as input the menu says air TV but it is not highlighted. It skips over this setting and will not let me change it.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic