An advertisement states that a machine with moving parts will continue moving forever without having to add any energy. Can this be correct? Explain.

Your question is asking about complete conservation of energy within a machine. Whenever there are moving parts in a machine, this is an impossibility.

Although the First Law of Thermodynamics states that energy cannot be created or destroyed in an isolated system, a machine isn't capable of retaining this energy (at least not with today's technology).  The problem lies with non-conservative forces--those that are path-dependent.  A common example of this is friction.  The amount of work done by a non-conservative force depends on what pathway it takes.  Think of rubbing your hands together.  The more you rub them, the more work it takes, and the greater amount of energy lost you will experience as heat.  

It is important to understand that work and energy can be looked at as very similar ideas.  Doing work to an object (applying a force resulting in movement in that direction) will result in a change in the energy that object has.  

In a machine, work is achieved from something like a battery, a spring you wind up, or something along those lines.  The machine is only capable of doing what it was designed to do with the work that was input.  As soon as materials come in contact, friction will result.  You hear this as sound.  Sound takes energy to create, and that energy is effectively "stolen" from the machine, never to return.  And this is only one example of the wasteful energy that machines must contend with.

So, unless the technology has some nifty way of recuperating that energy (and engineers work every day to do this!), the advertisement cannot be correct.