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There are plenty of opinions on various PC applications. I would strongly rely on the time tested results of public safety-Police Fire and EMS. Utilizing a ruggedized laptop, such as a Panasonic Toughbook would be my suggestion. They incorporate a gell-sealed and insulated harddrive to protect it from excessive road vibration. Most if not all "regular" PCs are not designed to be moved around and are extremely subject to HD failure, and unseating of components when exposed to road/mobile vibration and vigors. The power supplies, as previously mentioned are also issues. Stick with an OEM power supply designed for mobile applications.
As far as installing the PC, again, follow the lead of public safety I would recommend Jottodesk for their installation platforms. Run a google on them. I use their mount in my 2001 PSD 4x4 Excursion. The mount EASILY installs using the bolts from the passenger side front seat and can be installed in less that 10 minutes.
Back to the computer, if you dont need a pentium 4 processor, and just a basic PC, I'd check ebay or batboard.batlabs.com and look for a Motorola MW520 MDC (mobile data computer - or terminal) which is also a popular mobile application. I think it was made up to pentium 3 specs.
Anyhoo, I hope this helps you and others contemplating mobile computing.
I've been running a standard HP laptop for several years and on oilfield roads with no problems. But, that's why I mounted the platform on the seat - it cushions the rough ride. I also have the PC mount to plywood base isolated on 4 foam rubber blocks to further protect it from shock. Although I have an inverter in the truck, I run the PC on a commercially available 12 volt supply. http://www.targus.com/us/accessories_power.asp