I have gone from VGA to HDMI when connecting laptop via HDMI. Its a Sony Vaio and it does have a Full HD 1080 sticker on it, although max res is 1280 x 800.
With my new cable, I am able to set the resolution of my TV to 1920 x 1080.
Does than mean my LCD is capable of Full HD now? It certainly looks it, resolution is great, can see so much on the screen.