So you're saying when you plug in your computer to the TV with an HDMI cable, the TV doesn't recognize that your computer is there.
One thing I'd try is manually setting your computer to external display mode by using the "Windows Key + P" shortcut, if that doesn't work look around in your settings to make sure your TV is looking for input from the HDMI cable, I know that my monitor has several options and if I'm not on the right one I don't get anything. There can be a "TV" inpute, "HDMI" input, and "PC" input.