First of all: solid state for everything you possibly can. Dune buggy + Hard Drive = Head crash. Depending on the OS requirements and budget, you could either use CF cards with IDE adapters(up to about 4 gigs these are quite cheap, and will last more or less forever if you don't read/write them to death. Perfect for slim Linux installs, or cut down Windows with plenty of RAM and no swapfile). If you need more, you'd probably be looking at proper solid state drives. Seriously expensive; but they use them for a reason.
Next up, mechanical hardening: Fans are to be avoided if possible. I doubt cheap little case fans like vibration very much. A low power system will be easier on the vehicle's electronic systems, and easier to cool passively. Assuming you don't need too much power, the VIA embedded mainboards are pretty cheap and low power. Various specialty companies produce rather nicer embedded computers based on the pentium M; but those are considerably pricier.
Vibration will be the big enemy. You'll want to pay a great deal of attention to connectors, in particular. At very least, you'll want to physically secure the flash drive(s), RAM, power connectors, etc. You might even want to glue the RAM and flash in permanently. Honestly, I don't quite know how hostile an environment we are dealing with, so I cannot say how much you'll need for certain. Minimal would probably be solid state memory, RAM carefully clipped in place, the whole lot mounted on a good stiff plate and the whole case given intake filters and spring mounted. Tweaky, quite possibly excessive, would be to mount the motherboard, RAM, flash disk, and DC-DC converter on a stiff plate, pot the whole mass in thermally conductive epoxy, top it with a durable heat sink(not tall; but spread out over the entire area of the motherboard, and directly coupled to the epoxy, and then put a heavy mesh cage around the heat sink, to protect it mechanically. That would be a lot of trouble; but it would give you a seriously solid widget. A more or less totally solid lump, with connectors on one edge.
You might also consider looking into what sort of things the computer would be used for, and thus what ports, hardware, and software would make sense. Would they pretty much just be slapping a small screen and a GPS module on it(VGA and USB only, then)? Do people want to have a serial data logger and a bunch of digital I/O on the parallel port? Would they use 802.11B/G, EDGE? Would they need full Windows, or would embedded Linux suit better, what programs do they need, etc.
To my eye, it looked like a lot of those consoles were just GPS units glued(often elegantly, however) to the dashboard. I'd be surprised if you could undercut the cheapness and durability of dedicated GPS navigation systems, if that is all these things are. If you could, however, clearly define the advantage of a full PC, i.e. GPS, with serious logging possibilities + audio + system control and so on, and design a module that would cleanly expose the features and hide the complexity and delicacy of the computer(at least from those who don't want it) you could have a pretty cool widget.