Fortunately, this wasn't the first product demo I made :).
Check out the Mixergy interview with Miguel Hernandez of Grumo Media. He talks about some great tricks you can use to make simple product demo videos.
Basically, it's really good stock illustrations + some good Keynote work + a blanket over your head to cut out the echo as you record the voiceover on your computer. I actually really enjoy making them.
Thanks for mentioning my interview Frank!
If you are in a tight budget going the Keynote route can be very effective as well.
I think Frank did an excellent job given the time constraints.
I also interviewed him about how he made the video at http://grumomedia.com/grumo-inspired-demo-video-by-crowdsqua...
Most sites will have some good choices of illustrations. It doesn't have to be anything special. I really think you could get away with glorified stick figures and still make a great video.
The script and storyline is important. The big takeaway that I've gotten so far has been to make it "story-based". So instead of just a screencast saying "Crowd2 helps you create a marketing campaign to advertise your products", try, "Kevin is looking for ways to tell people about his new CD release..."