Press and hold both the Menu and Up buttons on your Apple TV remote control until the LED indicator on the Apple TV box flashes.
The LED flash lets you know that Apple TV is entering Black Screen Recovery mode. Apple TV will cycle through several resolutions to find the best match for your display device. Please allow 3 to 5 minutes for this process to complete and for an image to appear.
No, HDMI to VGA Converter does not change the resolution from its video source. However, if your VGA display does not support 1080p resolution you may need to lower the resolution from the source (ie. Apple TV).