In an effort to fix this hopelessly broken 2003 Dual-G5, I am going to 'oven' the motherboard this weekend. This may help reseat any surface-mounted chips.
I have a couple of YouTube videos saved, which outline the procedure, and should have all the tools and skills to complete the task. If this doesn't work, but I don't DESTROY the mobo, I am going to attempt installing an ATX power supply.
If anyone has better links to this procedure than the lame slideshow on YouTube, could you please post URLs in a reply. I am an absolute beginner with electronics, so an easier step-by-step guide would be preferable.