Product review (3 stars): Whirlpool 8194001 Door Balance Link Kit - screechy
This replacement kit fits my old Kenmore DW perfectly, including the two replacement pulleys, which on this kit now have two operable wheels vs. the one operable / one fixed wheel on the original.

This fixed wheel probably contributed to the cords wearing thin over time and snapping, I'm guessing due to the increased friction. Now, while two operable wheels may seem like an improvement, in this case it definitely is not. There's a very bad side effect: noise. As others have commented, it is simply awful. After installing the complete new kit mine emitted a loud screeching when opening the door. Imagine a horror flick sound effect amplified 10 times... relentless.

I tried adjustment - there is none - plus misc. lubes (5w-30, synthetic oil, white lighting dry chain lube) but zero improvement. So I simply put the old pulleys back on and tested for noise, one at time. That solved it, down to a mere creaking of springs. So I just left the oldies on. Looks like I'll be tossing the new ones.

I'd read of this screeching problem before ordering but hoped it had been fixed. It hasn't. My recommendation, save yourself say $10 and just order the replacement cords. Hopefully they last a few years 'cos my DW was bear to pull out.