So...should I just build a smoking desktop?
I'd really like to come in at or below $500; if that's not realistic, what is?
Never mind...the links from the links you posted answered the question.
I already provided a link about laptops... $500 for even a desktop is not going to edit at all well, and that would only be SD (Standard Definition) since HD requires a LOT more computing power
The notes below are about a year out of date, but some reading as a starting point if you want to build your own
PC I built for my wife http://www.pacifier.com/~jtsmith/ADOBE.HTM would do very well for Premiere Elements, plus scroll down a page or two for 3 price/performance level computers for Premiere Pro... these are, of course, MY ideas about what to build, if I was building a new computer for myself... YOUR ideas may wind up being different