VGA to HDMI prabably wont work, because the new Apple TV only has Digital out (HDMI + Toslink)
I use an HDMI to DVI cable on my Beovision 7-32 (It needs to support HDCP-Encryption) and the picture ist great.
In addition you will need a Optical to Coaxial Converter (will cost you approx 10 EUR) to get the sound into your BV7-40.
Depending on the age of your TV, you will need a software update too.