30$ would hardly pay for the board and chip set let alone the screen, wi-fi technology.. custom made boot loader and software to make it all work correctly. best way i could think of do this is use the core parts of a cellphone and try developing on a android operating system.. but even then the screen would not even be big enough for you to hang it on the wall and see.. i am more the capable of developing this but 30$ would be impossible.
Oh? I didn't know that... I thought this could maybe be made cheaply by using a small 10x5 cm LED as a screen, but for the rest, I have no idea...
Still, one could do the smallest/cheapest prototype possible, start a Kickstarter campaign, and try his luck with a reasonable price... If it fails, at least you have a ticker for yourself.