I think (please correct me if I am wrong), that the VGA projector port on the BV7 is for output, not input.
I recently connected the xbox360 to my BV7 via the component video cables (the 3 cables that look like the audio ones). It worked perfectly.
Alternately, you can get a DVI<->VGA adapter (costs a few euros), which will allow you to connect the VGA cable of the XBOX on the DVI socket of the BV7...
In both cases, you need to configure the input audio/video sources on the configuration menu of the TV...
Br,
Petros