What ports are available on the TV, and what other ports are available on the PC? Set-top boxes generally aren't designed to pass through a signal like that; I'd assume that HDMI port on your DIrecTV box is an output, not an input.
The port on the Sate-lite box would be to plug the sate-lite box into the TV through HDMI. This would be the only reason that it would be on the Sate-lite box. For instance if you had a monitor with HDMI you could plug your Sate-lite box into your monitor and you would be able to watch Sate-lite television on your monitor