Product review (5 stars): I started at Kitchenaid's web site to get the exact ...
I started at Kitchenaid's web site to get the exact replacement part number before looking on Amazon.  There were two cords and two roller units in a clear bag labeled "WHIRLPOOL CORPORATION FACTORY CERTIFIED PARTS" and "Consumers Deserve It!" along with similar phrases in French.  Other identifiers read: 8194001, LINK, code 140209, 4391723 Rev C and a mailing label with B0053F9V20 00-8194001.

I think the old cord stretched about 3/4 inch before breaking, so don't be surprised if the new cord is shorter.  Whirlpool upgraded this part with a second roller on each side in place of the higher-friction channel.  This is a one-person fix--see online videos and bring your safety glasses and your vise-grips to extend the rear spring so you have enough slack to attach the cord in the front.

If I had known this would cure the metallic wailing sound we got with every movement of the door, I wouldn't have waited for the cord to break!