Broken BF Rich Window Part

Looks like you need a new coil balance. We should be able to help with this, but I will require a photo of the pivot shoe in order to make a recommendation. That will give me a better idea of what this assembly is and what part in our inventory will work. 

The pivot shoe is the square or rectangular block immediately below the piece you've shown us already. It's what connects the springs to the sash. You can see our full selection of pivot shoes here.

That's unfortunate. I'm afraid that I can't ID what coil balance you have without seeing the pivot shoe. It's a key component.

Do you have an identical window in the house that may still have all its hardware? If so, we can use that as a reference.

If you really have no window in the house that has a pivot shoe we can see, then your next step should be to contact a local professional who is familiar with homes in the area. They can hopefully point you in the right direction.