Not permitting me to take our vehicle from the branch even though they have been unable to make the necessary repairs on our car since Septermber 2023

We took our vehicle to this branch in September of 2023. They informed us that they would need to order the part to make the repair. It is now February 16 and the part has still not arrived. We've been inconvenienced by not being able to use our vehicle for over 5 months. When going to the branch today to take the vehicle since they have been unable to fix it in a reasonable amount of time, they refuse to give it over stating we need to pay for the part that was ordered, even though this part has not been put on our vehicle. How can we be made to pay for a part that our vehicle is not repaired with?? This is extremely unprofessional and bordering on *******. Do not use their services, you will be extremely disappointed.