Why not just buy a netbook at walmart for 289$? I mean, really, this thing is going to be a monster.
A more serious answer to your question would be more like a via nano board with a compact flash adapter or even a cheap SSD.
VIA Eden-N Processor - VIA Technologies, Inc.
Maybe even a gumstix single board computer.
gumstix - dream, design, deliver
I understand that the original xbox stuff is cheap but man your asking for it if you try to go this route. You say you want to use a laptop battery. That smells like disaster to me. You do understand that Lithium Ion/polymer batteries have strict charge and discharge requirements. Not meeting these requirements will at the least ruin the battery in short order and at the worst burn your house down.
Also, be aware that the power requirements for the xbox internals are much more complicated than just providing one DC voltage. You will need to provide +12v,-12v,+5v,-5v,+3.3v,-3.3v. Just like any standard PC. I'm not sure about the exact internals of the original xbox but it is basically an intel celeron with some specialty chipset developed by Nvidia.
I wish you good luck in your endeavor.
