No, the Dell Vostro 3700 does not have a TV Tuner. The HDMI port you are referring to is the secondary display output. You will need to use an HDMI cable from your laptop to the TV (assuming the TV has an HDMI input) and enable the TV as a secondary monitor on your laptop. You may need to adjust the resolution of the secondary display in order to get an image onto your TV.
That should be all that's necessary.