Acquire: He's Dead, Jim

If you have given any number of presentations or speeches you have likely encountered an audience that was non-responsive. This could be anything from a little distracted to active hostility.
So what do you do?
Firstly, I'd like to offer that I don't think that leaping into your interpretation of an actor tearing up the scenery is your best choice.
Secondly, take a moment to check-in with yourself. Have a sip of water, make sure you are breathing efficiently, scan for physical tension or body language that may be telegraphing more that you'd like to the listener. Now is a time for focus and authenticity -- you can panic after the meeting if you need to.
Next, my suggestion is to insert a disruption and try to shift the dynamics in the room. This could asking your listeners to stand (of they are able) and stretch, or do an exercise. Perhaps there is a series of questions about the listeners and what they care about. If you are lucky, one of them may give you the information you need to shift their thinking. Importantly, engage the Humans in front of you.
Whatever device you use (and I suggest you think about this well in advance of your presentation so that you have some ideas cued), make sure that you are still leading and directing the space from your strengths.
Conclusion
If it doesn't improve, don't take it too personally.
Your audience might be exhausted. Perhaps, they are being forced to be in this meeting or workshop. Maybe they just heard that a beloved co-worker has been fired before your workshop (this one actually happened to me). In other words, you can accept the possibility that it is your presentation (in your post-game not during the event) but don't assume that to be true.
Do you have any stories about dead rooms that you revived, or not? I'd love to hear them.