There are two ways to build something like you are looking for.
The first: A small motherboard, such as a Mini-ITX, or even smaller Nano-ITX with a power supply such as an OPUS.
small, easily built-into little spaces (dashboard, glove compartment, etc.)
low heat, for those little spaces
low power requirements, smaller power supply needed
not very upgradeable, due to limited PCI slots (may not be a problem)
limited power (but powerful enough to run most carputer applications)
The second: A large, full blown desktop PC system with either a larger power supply, or an inverter
can be upgraded (more PCIs)
as powerful as you want to make it
can play Halo 2, Doom 3, etc. (extremely useful on the highway)
require much larger power supplys
There are store bought options for each. But, you really ought to