The Raspberry Pi is a popular open source affordable computer. It even has third party kits to connect and drive official LEGO® motors. While you can build a case out of authentic LEGO® elements, it looks like someone has developed a case with compatible studs built on. Having built a case out of LEGO® bricks myself, I can say from experience that the slimmest design I could make was not particularly easy to use, so a form fitting case like this may be perfect for your project.