Hello Kevin,
Firstly - welcome to
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I like your idea, and it should be possible to do. However, it would be useful to know what operating system your laptop is running before we continue.
As for small computers - you may want to look into the Asus eeePC. The older models with the smaller screen are only around £220-240, and with the new model being released soon the price should drop. It's about the size of a paperback book and would sit happily on a car dashboard.