Making A Easy-To-Setup $50 Linux Multi-Seat Computer

It's not a computer. It does not perform any logic operations. (unless you are referring to the actual central computer, in which case that will cost you much more than $50)

These things already exist. They're called station hubs, and you can buy them from Wyse/Dell, HP, and other retailers for less than $100.

I'd be very interested to see one be sold for $50 dollars, but I'll believe it when they're actually being sold at that price.