From looking at these photos I think I?m in the same boat as this gentleman. My balance looks identical to his. There is a small metal hook on the end of a nylon cord at the bottom. No plastic clip whatsoever at the top. There is a metal cap that screws directly into the side of the window frame which acts as a cover at the top of the balance. The balance is stamped 2840J on the side. The balance is 29 inches in length.
I?ve added some photos. One shows the top of the balance which is still installed. The others show the one I removed (and broke in half). I?m not sure how to get the other one off without destroying it either. Any help with replacing these and getting my window back in working order will be met with thunderous applause and undying gratitude,