Is it right to be charged for the piece that did not make my laptop work, even though I agreed to the ordering of it in the beginning?

I recently took in my laptop (2006 mac book pro) to get looked at. I was having problems charging the laptop, even after buying a new battery and power cord. They checked it out and said I needed a new part (i forgot what it is called), then gave me the price of what ordering the piece from apple would cost, along with the repair cost. I agreed to go along with ordering the piece and pricing. A couple days later, I received another phone call from the computer repair specialist saying that the piece did not work, and that I would need to order a new motherboard for it to work. I did research, and realized that I was able to buy a better used mac book pro online, for a cheaper price than what repairing the motherboard would cost me. In the end, I decided that my best option would be not to go along with this repair, because I would be losing money, rather than investing on something I could potentially sell later on.

My question is, is it right to be charged for the piece that did not make my laptop work, even though I agreed to the ordering of it in the beginning? I would appreciate any feedback.