(BTW, I have been aware of the nano-ITX boards for months now. It's no different from any other type of motherboard though as far as using the PSone LCD. You either need to be able to do a VGA mod or be in for a world of hurt using TV out. Say hi to Handicapped Mode)
However, some caveats:
I admit you probably don't NEED a keyboard. There are soft keyboards out there.
There are also other keyboards you could use. I actually have one in mind that if you insist on doing it, you might want to look into:
This might actually be feasible. But... yeah, considering how thin and small laptops have gotten lately... you're still never gonna get something like that down to the size of even those. (BTW: I've seen these controllers here for as low as 10 bucks. They're probably all sold out now, but just letting you know that 40 is a bit outrageous.)
Battery life would suck balls. Honestly. Even a nano-ITX board is gonna take something like 10W without anything even hooked up to it. Including your PSone screen! Input devices, etc. will take even more. I'd say you'd be lucky to get it even up and running and not drawing less than 20W. And how many watts does the typical portable draw? Well, let's just say it's probably an order of magnitude less.
gannon: Even the nano's onboard chips probably draw more than anything portable out there at the moment. The C3 Eden processor itself draws 4W or so (about double as much as a PlayStation 2, IIRC). Not to mention that probably all of the chipset logic and onboard video even takes about 5W typically. I'd say at best you're looking at a 10W draw. I definitely think Epicenter was way off base with his wattage calculations (I think the Dreamcast is only probably 2 or 3 watts max without the drive... it's really pretty slow and dedicated). I am a big fan of the CF drive idea though
Though I stick by what I said- battery life would either be abysmal or you would need a HUGE battery setup... not to mention the power supply card... which would also take up yet more space.Then again... I wonder how many watts a PS2/Dreamcast takes with the drive... you might be on to something there. If you can get away with only the CF drive.
cennar: You're not going to beat the big guys at their own game here. My laptop fits into my hand
I'm holding it up with one hand as i type this sentence. I should say that I think it is possible, but if you think you're gonna beat the laptops in size and usability... you're out of your mind.And just because I'm new to these forums does not mean anything about my technical capabilities. I've got a bachelor's in CS/Engineering. And I've been using computers since before you were born. (Admittedly I was basically using them to play Donald Duck's Playground, but still.)
I've built more computers than I have digits--not including ones I've made specifically for others. So don't treat me like I am ignorant.
In short, good luck
Despite all of my pessimistic comments, I hope you do succeed. I am definitely looking forward to seeing the results.Hope I didn't come off as too much of a (insert some expletive here that isn't blocked) before... but this really does sound pretty... less than doable with stock parts. Design your own custom motherboard and you might be getting somewhere
What'd be really amazing is if you could wire mouse signals to the right joystick of the PS2 controller and still keep the rest of the controller usable for gaming 
In short, it's not impossible, but it'll be so huge that buying a laptop would be the better option.
