Hi, I realize it's been a while since the original post but the perfect kitchen computer is at hand. The Always Innovating Touch Book, http://alwaysinnovating.com/home/index.htm. It's small with an 8.9 inch screen. It's fanless - don't have to worry about cooling. It's only about 1 1/2 inches deep and can be easily mounted in the wall or under a kitchen cabinet with an LCD under cabinet mount with swivel. If you want you can even mount it directly on the refrigerator - it's backplate is magnetized.It runs linux and can serve up web browsing and 720p video.
Best of all, it's only $299 without keyboard. This is the best way to go in the kitchen and should be available early this sumnmer.