Yes, A body can have energy even when it is not in motion or doing work.
For example,
When a body posseses potential energy , somewhere in sky.
OR like you throw a ball in upward direction,at the topmost point, it will have its final velocity(v)=0. But it will possess potential energy as it is at some height and gravitational force of earth act on it.(Potential energy=mass of body × gravity(9.86) × height of body from surface.)