When does an object possess mechanical energy?
can be more than one

when it has the potential to move
when it is moving
when it is stationary
when it is fixed to a specific location

Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position (for example, a brick held at a vertical position above the ground or zero height position). A moving car possesses mechanical energy due to its motion (kineticenergy).