I'm a newly minted ham myself. I got my ticket this past March. Anyway, if you'd want to split the HDMI into right and left audio and VGA you could try this item from monoprice, it's $38.25, so not too steep. http://www.monoprice.com/products/product.asp?c_id=101&cp_id=10114&cs_id=1011410&p_id=8126&...

Sounds like you've covered all your bases power supply wise, the battery test ends any question about the hum being introduced by the power source. Does the hum go away if you power down the display that the GUI is running on? If not, it would seem pretty likely to be something on the Pi, as long as...

I don't think you have a bad board. I've seen this happen on a lot of PCs and media devices over the years. It's just that the audio jack is picking up feedback from the display. Are the audio and video cables running close together in parallel (or touching)? Do you have the volume set to a very hig...