"Finishing something" means the task is complete. In this case, yes, it means the repair is complete, and the car is in working order.
If you intend to say that you stopped the work before the repair is complete, you could say one of the following, depending on the situation.
- I paused my car repair until my next paycheck.
- I'm holding off on finishing the car repair for now; original Mustang parts are hard to find.
- I quit working on my car for the night, I'll start again tomorrow.
- I bailed on helping my brother repair his car; I think I'm just getting in his way.
This last one is slightly different, in that you are "bailing" on someone (your brother), not "bailing" on the car repair itself.