About a year and a half ago I acquired an IBM Thinkpad 340CSE, one of the budget models in a long series of Thinkpads known for their thick and blocky shape. It wasn't functioning, but I was intrigued by the possibilities it presented: it's very sturdy and there's easily enough room inside to fit in a Raspberry Pi (or BeagleBone Black) with a battery and USB hub.
The photo above is a Thinkpad 360PE - I needed a publicly licensed image (in this case borrowed from Wikipedia) since mine is in pieces. There are some slight cosmetic differences (mostly because the 360PE was an early convertible tablet, note the pen), but the overall appearance is essentially identical.
While a lovely idea, this isn't going to be simple. The keyboard and screen are the two big challenges: I think I can handle the screen, although it'll be annoyingly expensive: 10" LCD HDMI screens are a bit difficult to come by as people usually want them larger (around 15") or smaller (for portable projects). But they can be found. And the hinges are well designed and should easily support the necessary cabling. No, the keyboard is the big issue. A replacement keyboard seems like a bad idea because nothing will fit: a wireless keyboard would be clever, but I've yet to find one narrow enough. I would much rather re-use the original keyboard. Look at the thing: those keys have nearly the full throw of a standard desktop keyboard, and a feel better than any modern commodity keyboard.