sash slider track?
From what you've described, it sounds like you need a new jamb liner. I'm afraid we are not able to sell those. I recommend contacting a local mill work who still makes wood windows for assistance.
Now, if the balance inside the jamb liner is all that's broken, we can help with that. Based on your second picture, your nylon shoe is similar to our 15-014. This shoe is commonly used on our Series 751 ribbed channel balance. I cannot guarantee that this is what you have without seeing more of your balance, but it may be worth considering.
Don't worry about the number of cords used in the balance. The exact configuration of the guts doesn't matter so much, just the primary physical details, such as the design of the metal channel and the design of the shoe. The spring strength is also important, and it's indicated by the stamp printed on your balance.
As for how to replace these, see the video below.