You may need to update the drivers for your card before you can use the hdmi port on your card.
A few things to check:
-Is your pci express card properly inserted into the corresponding pci-express slot?
-check with your motherboard manufacturer for a 1.0 or 2.0 slot difference.
-Do you have all the updated drivers?
-check This Website for Your card specific drivers AND download the Nvidia Control center to get everything properly configured for your tv.
-Is your display resolution outside the resolution range of the tv. If the tv is a 1080p resolution, the max it can support is a resolution of 1980x1020. You can view a tv resolution guide Here (yes its wikipedia, but its a very good chart.)
In windows 7, right click anywhere on your desktop and click screen resolution.
If the above option is your case, set your resolution on your monitor to a displayable resolution for the tv, and then switch the cable over to the tv. This may require a restart.