I think it would run a version of linux designed to boot quickly and require minimal user intervention (ie a nice graphic display controllable with a joypad used to select items on screen) so the user has the benefits of a console and a pc without needing to be a pc savvy person.
I think a 1.5 Ghz cpu, 40 Gb hdd, low cost Nvidia gfx card with tv out (say one of the 6600 series?), wireless networking card and digital joypad would be good.
While it is true such a thing is essentially a pc it is a very user friendly one requiring minimal user knowledge and intervention and people would pay for a decent console system able to play films, music, games, emulators etcetera out of the box.
That`s one thing that attracted me to the GP2X and before that the Xbox (once it had been altered to have XMBC on it).
People will pay for an all in one unit :)