Check out the new Intel Dual-Core Atom board: Intel D945GCLF2 Dual-Core Atom
It has S/PDIF digital out.
Put it in a mo-co-so case with an M2-ATX power supply.
As for xbox, use the composite video output, and hook it up to the second video input on whatever monitor you plan on using, and switch the video source on the monitor between computer and xbox. The audio can go to line-in on the motherboard, so it will play through the amp.
That board has a serial port, so get a serial GPS receiver, they are more reliable than USB. Unless you plan on using HD Radio, that requires serial, so you would get a USB GPS receiver in that case.
Hope this helps!