I just want to run a CPU on it. I do not need to send instructions, because the entire program fits into cache. So only an interface that could provide some basic I/O and some code execution after being powered on.
You need to tell us exactly what you're trying to do.
The Arduino has inputs & outputs. There is no operating system and it runs a single-program from flash. It's a microcontroller board, not a motherboard. There is also no standard keyboard, display, or file storage. These things can be added (to some extent) but without an operating system anything like that has to be custom-connected and custom-programmed.
And, the Arduino isn't fast-enough or powerful-enough to process audio or video.
For example, you CAN use an Arduino to blink an LED sequence when you push a button, or run a motor when the temperature is above a certain temperature., or you could blink an LED sequence with no input at all... By adding some solid state relays or some dimmer circuitry the Arduino could control stage lights... Things like that...
These kinds of specialized applications are called [u]Embedded systems[/u] or embedded microcontrollers.
The thing that makes the Arduino unique is that it's a complete board with a microcontroller chip and a preprogrammed bootloader, and some support circuitry. That makes it super-easy to use (compared to a raw microcontroller chip 
). Microcontrollers are generally sold as chips and a custom special-purpose board has to be made. Modern cars usually have several embedded microcontrollers. All of the boards are different and the boards (and chips, and software) in a Chevy are different from the boards in a Ford, etc.
Although the Arduino uses a "little" 8-bit chip, there are some very powerful microcontroller chips and of course you can build an embedded system with the same Intel or AMD microprocessors that are used in powerful computers or servers.
If you want a "motherboard" you might be looking for a "single board computer". These are more powerful, they can run an operating system, they do support a keyboard, mouse, display, and file storage, etc., but of course you're not required to use any of that and you can use an SBC in an embedded system (very common actually).
