To repair the broken tractor on Ray's Farm in The Genesis Order, the broken Drive Shaft must be repaired. You get the crafting recipe for this directly from Hannah in the barn.
To repair the Drive Shaft you need a Bearing, Grease, a Rubber Boot, and the Broken Drive Shaft. The Bearing can be found at the Warehouse on the right side on top of the container. You will need the Jump Shoes to reach it. The Rubber Boot can also be found at the Warehouse on the right side behind the bushes. You will need the Machete to get the bushes out of your way.
You can buy the grease at the store. On the table in the barn of Ray's Farm, you will find the Broken Drive Shaft.
Once you have crafted the Drive Shaft you can return to the barn and the story continues.