Render just part of a final image from Cycles? I'm using an older Nvidia chip that hates running viewport renders, and I need to check if changes to the materials on a few objects not far from the center of my scene are (I'm rendering a floorplan with an orthographic camera from above, so I'm looking down on objects and want to check if the displacement materials are working correctly).

Is there any way to select a bit of the image and have it render first or without having to render the rest of the image? I'm aware that you can tell the image to render from an edge, but my stuff's about equidistant from either side of the scene.
Ctrl + B in the 3D Viewport or the Camera View will allow you to drag while holding  LMB select the area of the image you want to render. If you want to clear the border, press Ctrl + Alt + B.

Shift + B also still works in Camera View but is only there for compatibility and will be replaced entirely by Ctrl + B in future versions.

For "Render->Render Image" (F12 ) to render only part of the image you also need to have Render->Dimensions->Border enabled.