Do I have to move a vehicle on my property if asked by the landlord? How?

If it is not working it is not your transportation at this time. If your lease says you are entitled to a parking as opposed to a storage space, the landlord is probably correct as it reflects poorly on the property value to have an unmovable vehicle sitting there. The issue is one of what your lease permits.

Generally Motor vehicles must be able to run or the city will fine the landlord. See if you can get an extension by landlord or the city otherwise you may have to pay the fine or find somewhere else to park the vehicle.