In order for a car without keys to be shipped the following conditions must be met. If these things cannot happen a tow truck or a forklift will need to be hired for an extra fee to load the car onto the car hauler. A local tow truck may also be necessary to unload the vehicle at the delivery location.
For a car to be loaded or winched onto the trailer its wheels must be parallel to each other and pointing straight. If you can’t turn your steering wheel it is probably locked due to the anti-theft security feature or the steering may have been damaged. If the wheels are turned to the side a tow truck will have to be hired to facilitate the loading process.
For a key-less car to be transported its transmission must be in neutral gear so it can roll without resistance. This is not an issue with most cars and manual transmissions, but some automatic transmissions require a key to do this. In certain vehicles it may be possible to disconnect the transmission shift linkage to reach neutral.