Ok, what you probably need to do is change your desktop resolution for the computer, but do this when the HDMI cable is plugged in. You can do this via the Windows settings or depending in your graphics card there should be some settings for it which will also let you set the resolution.
What operating system and graphics card do you have?
There will also be options to tell your computer what to do when you plug in a second display/TV - you should be able to change something here that will stop the image disappearing from the computer screen (if that is what you want) and whether the computer screen and TV screen should display the same thing or whether the TV should be treated as 'extending' your desktop.
My guess is that you need to play around with the settings in these areas to try and get things working.