So I found this article on HackADay.com that discusses how to build a small computer on a PCB about the size of a business card. So I went ahead and managed to order a PCB for it and all the parts.
It took me awhile to scrounge the stuff together, but eventually it all arrived. Then I spent a very careful 10 hours soldering on all the tiny little surface mount components. I must admit, this was a great introduction to that world. Anyway, here’s a YouTube video I made just showing this thing hooked up to some power. At this point, I don’t have a programmer, so I can’t actually program the board to do anything other than look like a work of art.