Can you even get your Windows desktop to show up on the TV, or do you have an easy way to compare with another HDMI monitor?
It really shouldn't be too much different than hooking up an external monitor with your other outputs which you might even want to try if you haven't already to confirm this works at least.

This may not be too likely, but if you can't seem to get any HDMI output from your G74Sx just make sure the cable is securely plugged in all the way into the notebook and there aren't any issues with the HDMI cable you are using to do this. This may have been an issue with a different kind of cable, but I vaguely remember an issue where some cables didn't allow you to plug them as far in because of the design of the cable although I would think most cables are designed similarly these days.
Well, if you have an easy way to try another cable, may be worth a shot. Good luck!