Sounds like your cloning the main laptop screen to the TV.
I'm assuming you're running Windows Vista/7/8 here. If not, let me know :)
- Right click desktop -> Screen resolutions
- Multiple displays: This should be "Extend these displays"
Important: Click on your laptop screen above (press Identify if you're not sure which screen is which number) and tick "Make this my primary display". This ensures the task bar shows on your laptop screen.
You should now be able to drag your media player application across to the TV (usually the right, but check how they are arranged in the Screen resolutions form), whilst having your web browser on your laptop. You won't see the video at all on the laptop.
I have this as a permanent set-up for my desktop PC. Main monitor on my desk for doing stuff, and a TV on HDMI for watching videos.
You should also set the default sound output to your main speakers and not TV HDMI, then in your video application set that to output to your TV HDMI. Then you can have your TV just playing sound from the video. If you're not sure how to do this let me know too :)
Edit: Once you have dragged over the media player to your TV it may save its' position there. Media Player Classic certainly does this, and is ideal for your situation. (it can remember the monitor to use, where to be on the monitor i.e. full screen from ALT+TAB, and the sound output) Not sure if Windows Media Player or VLC behave like this.