After some discussions with Steve Dembo (@teach42), he told me he had used a device to do this already. I did my research, did some reading, and decided to try it out. The device I used is called the "LinkStyle HD Video Converter" and is available via Amazon.
A couple of notes:
A simple VGA to HDMI connector will not work for this purpose.
For hookup to a television monitor, you may need a pin-pin VGA cable. (The converter box has a port, as does my television.)
Since VGA does not carry audio, you will need a separate audio cable. The converter box has an 1/8" jack (headphone and computer speaker size) for audio out. You can plug speakers right into the converter or use adapters to get it to whatever your audio output device needs.
It was easier to create a graphic then explain the process, so you will see that below.
|Click on image to enlarge|
Addendum (5/2/12): This VGA to HDMI device, the Kanex ATVPro, apparently works with AppleTV with no power source....nice solution!