Super-ultra-bare-bones for writing

I want to build a second machine almost entirely for the purpose of writing. My main computer is fine, but I have crazy ADD and don't get shit done when I try to do any writing on it because there's so much to distract me.

Anyway, my plan is to build something mini-itx and just run some flavor of linux. Any reason this wouldn't be totally OK? I just need something simple and serviceable.

You should go to your local salvation army or good will and see if they have any ancient PCs that you can install linux on
all you really need is a text editor like vi, then you can save it as file.txt and put it on a floppy disk
copy it into word and change the formatting so it doesn't look like shit
also, EEE is perfect for writing; small keyboard though