System on chip to replace notebook motherboard

I have a couple of broken notebooks and would like to know if someone has tried to replace a notebook motherboard with a system on chip that the keyboard and screen can be attached to. It doesn't matter what architecture the SoC would be since it only has to be able to run a lightweight Linux desktop. Recompiling applications would also be a pretty trivial thing to do.

The only other requirement would be that it has to be small in order to fit into the notebook enclosure. As it is now, notebooks are too fragile and spare parts are not readily available, expensive and sometimes already EOL. An ideal situation would be standard notebook form factors with interchangeable cheap parts, just like desktops.