look up "gumstix"
They're pocket PC's based on the Mini-ITX platform, but taken to a much smaller extent.
The "full system", as it were, is no larger than a pack of cigarettes, until you add your peripherals.
One of those will have similar system capacity to some of the 90's computers that were capable of running games like Doom and the like, but will still be capable of multi-tasking due to newer technology. They also don't require cooling. Simply placing the system in open air is enough. Occasionally, if it gets too warm, blowing lightly on the CPU will bring the temps back into range.
Something else you might consider is a human powered generator system for your trade shows where batteries are a problem. The lanterns that you wind up which have self contained batteries could be modified to pass current rather than produce light, and between customers, you could get a light workout by cranking the handle.
The gumstix PC systems run on DC naturally, and an AC adapter can be purchased separately, similar to a laptop charger, so the lantern and a DC/DC converter should be more than sufficient to power the <20w models, not including your monitor and periphery.
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