Don't use stories: use storytelling
Stories are compelling, but you don't have to overwhelm your presentation with examples. Rely on story structure instead. Start your presentation with the Problem.
Don't underestimate this: though you may have a great solution, you'll first need your audience to care. Once the Problem is assessed as your villain, you can introduce the hero: your Solution!
And then comes "the duel". Inform your audience of the time and skills that you and your team put into solving the Problem. Explain why and how your work is valuable. Finally, nothing works better in stories than a cliffhanger: what shall we do next? That's the Call To Action, a clear next step demanding that the audience takes part in your story. Perhaps having your project greenlit.
Choose an online tool
Since it’s called a “presentation”, style does matter. Even your most cunning-minded boss is not immune to a fancy slide which is really fancy - nor he is unlikely to grow uninterested by a mundane dotted list.You may not have the latest software installed, but you certainly have an internet connection. Google Slides is your classical presentation software - only free, and easy to use for workgroups. For something different you can give a shot to Prezi: a unique tool that could take a little longer to get familiar with, but is indeed holding great potential for high-impact presentations. Or, you can still count on your beloved Powerpoint - the online version of course, which is collaboration-friendly and most of all, always up-to-date.
Share your presentation, not just your slideshow.
Your project may need to be discussed further or thought thoroughly about; or a key player may have missed the meeting. These are just two reasons why you might want to share your material for remote viewing, and online-based presentation tools are very helpful with that - without mentioning other services such as Slideshare. And yet a presentation is you talking, with your deck of slides helping engage the audience - not the other way around. That's why you should film your speech and share the video together with the slides. Can't film during the actual meeting? Record your last rehearsal.
As a final suggestion, don't forget to copy from those who got their solutions approved: search some examples of funded startup pitch decks, real troves to learn what works. Better said, what calls decision-makers into action.
Will your project be next?