You do not have a problem with any cable, converter, LED, monitor, speaker, keyboard, pet dog, refrigerator or mouse - just to head off any other crazy unrelated guesses you might have.

The cable supports conversion formats up to 1920×1080 (1080p Full HD) with max refresh rate of 60Hz and 1600×1200, 1280×1024 for high definition monitors and projectors.

Solder the wires from the VGA cable to the Xbox 360 connector using the pinouts provided to match up the signals. You can connect all the VGA ground shielding to a single ground spot on the Xbox ...

DVI and VGA are both incapable of supporting an audio signal, even if they're converted to HDMI (which does support audio). To get audio, you'll need to use a separate audio cable.