The LCD TV might have a VGA connector on it as well as HDMI -- so if that is available (Most Samsungs and a load of other TV's designed as well tom be used as a computer monitor) use that connection. -- For sound in this case plug the headphone socket from the computer into the AUDIO IN on the TV -- you might need a mini-jack to two phone lead connector.
The VGA ==>HDMI converter DOES work but it upscales -- so the quality of upscaling will depend on the quality of output from your computer.
The other thing I'm not sure is what resolution you need to set your laptop to for VGA -- 1366 X 768 seems pretty standard but any less you'll get some funny shaped output on the main TV screen unless you have in the picture settings "Automatically adjust" which will try and optimize the picture size.
Here's a cheap one from UK (the cheap one's IMO though have a very poor A/D converter) VGA to HDMI Adaptor | Clas Ohlson
pay slightly more and the results should be a whole lot better. Search results
(Considering new laptops are quite cheap these days - it might be better to upgrade your laptop if you will be playing a lot of HD video content).