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First thing you should do is to make sure that you can get output from the vga port on the laptop to a regular computer monitor. You have to get the VGA port to produce the output..Yes..it's required. Once you can confirm this, you will know you have the steps down to enable that vga port.
Then once you get that working, introduce the adapter and connect it to the laptop and TV. One thing that is critical is to make sure that the resolution on the laptop is not set higher than 1920x1080 because that's the max an HDTV will support. Go ahead and set it to the lowest setting just to test and see if you can get output...you can incrementally change it later. That's pretty much all you do. There's no drivers involved at all. If you still get no output after that, I would question if the adapter works at all.