It all depends on a few factors.
Firstly, what components you decide to use. If you use something like the VIA Epia range of boards, then they are designed for low power usage, so they won't consume as much juice as standard desktop components.
The other thing that affects it is the power supply you use. The most efficient thing to use is a DC-DC power supply, such as an Opus, or if you have a case with the Morex 55W DC-DC PSU (which will be in most of the "Mini-ITX" cases you can buy) then you can use the Carnetix CNX-P1260, both of which will give you >90% efficiency. This means that of the power that comes from the battery, over 90% of it will be used in the computer, and less than 10% will be "wasted" in the conversion.
Compare that however to the other option, which is an inverter and a standard PC power supply. Most inverters will be around 75% efficiency, and add to that the PC power supply will be at best 75% efficiency, so using this setup, you'll be pulling over 150% of the power you need to just run the system!
So, best bet is a DC-DC power supply, and depending on what you use, depends on how long it will last. I would estimate (but it is only a complete guess) an Epia setup will probably pull about the 150-200% of the power that a basic, standalone DVD/LCD will do, because of the nature of running a PC
However, if the engine will be running, then it doesn't really matter, as the alternater will be charging the battery all the time