Totally agree with Craig McClure
here, there are great DIY solutions out there but they will never replace a professional who took your idea and crafted a personalized video. Yes that can set you back as much as 2-3'000 usd (that should be the upper limit, in your case it sounds like less, you didnt specify what you'd want to show) but it will be your voice, talking to your potential clients in exactly the imagery you wanted.
Of course, since you said "start-up", what many people fall back on to explain their product/service pre-funding stage are whiteboard animations, they can be emotional but usually they are a great way to demonstrate your business to potential clients/investors at a very early stage.
We offer inexpensive whiteboard animations so get in touch if that's what you're looking for (or just google one in your area), but the best advice is to get a professional to help you.
And let us know what you went with! Would be interesting to hear what worked for you out of all of the good advice given here