Are you an inspiring leader?

I was working with a client the other day who consistently complains about the lack of energy in their workplace. It is an organization that has its problems and lack of energy is definitely one of them, however,  I did start wondering what this person was doing - in their leadership opportunities - to motivate people.
If tasked with standing in front of a group of disengaged people how do you respond?
Do you see it as hopeless?
Do you go through the motions with no expectation that anyone will become engaged or be interested?
Or do you take a deep breath, hitch up your pants (figuratively if not literally) and set out to connect, engage and motivate the group in front of you?

Having been a trainer for adults, a middle school and high school teacher and a counselor for troubled teens I have many years of experience of standing in front of disengaged and disinterested 'learners'.
Without question there have been days that I looked at the slump-shouldered people in front of me and thought, "forget it, nothing will happen today". But then I would remind myself that my 'job' was to get my message across.
I would recall successful training sessions where the room was buzzing and light bulbs were popping on the entire time. I can feel that energy just thinking about those times.
Bottom line is that I change my mindset from feeling defeated by the dark cloud in front of me to seeing it as a challenge.
Sometimes its a really, really big challenge.
For me a challenge is really motivating, it energizes me and starts my wheels spinning to find ways to use my energy to ignite my audience.

In my mind I am trying to inspire. I am trying to move the disinterested to be interested. I want to motivate those that have stopped caring about the quality of their work and their contribution to the organization to start caring again.
Because if the fifteen people in front of me become inspired and motivated they take that positive energy back to their teams and that offers potential for others to become more caring and motivated.

So how do you inspire the uninspired?