Possessive

There's a car engine sitting on the floor of my garage and I would say:

1. The car engine is still in good condition though it looks old.

If there's a car instead of just a car engine in my garage, to emphasize that the engine belongs to the car, I would say:

2. The car's engine is still in good condition though it looks older than the car itself.

If my interpretation is correct, #1 shouldn't take the possive form because it misleads the listener to think there's a car in the garage and the speaker is refering to the engine in the car.

Is my usage of the possesive form correct?

Thanks in advance!

Do you mean you don't agree with my interpretation hightlighted in red below? What's your interpretation then?

There's a car engine sitting on the floor of my garage and I would say:

1. The car engine is still in good condition though it looks old.

If there's a car instead of just a car engine in my garage, to emphasize that the engine belongs to the car, I would say:

2. The car's engine is still in good condition though it looks older than the car itself.

If my interpretation is correct, #1 shouldn't take the possive form because it misleads the listener to think there's a car in the garage and the speaker is refering to the engine in the car.