I checked the manual on my G55 and it mentions the HDMI port, but doesn't specifically say if you can plug it in while on power. However, in my experience in the past with my other Asus laptop with an HDMI port, I've never powered off my machine to plug in to my TV and I've never had a problem. I believe HDMI is a plug similar to USB.
what i do whenever i watch movies on my 40inch mostly HD movies is i use Set Mutliple Display from Nvidia Control panel, and switch the output to my bigger panel, then automatically the laptop panel will turn off, unless youre doing a mutliple display or something else that you would need 2 monitors.
Ok, one more question: My G75 display is 1600x900 max resolution, the TV display can do 1920x1080. If I set a game to use the 1920x1080 resolution of the TV display, then quit the game and forget to set it back to 1600x900, then start the game using the G75 display with the game still set at 1920x1080, what would happen. Would it damage my display? Just not start?