I downloaded the file and listened to it. It sounds like electronic static of some sort. In have no idea what would cause it or whether it's normal or not. I've used any digital camera in movie mode. But I do think there's a problem. Whether it's within Canon's specs is another issue.

I think, if video is very important to you, maybe you should invest in a dedicated DV camera. Your G3 is one of the best compact digital cameras. But video is just a bonus. It's not what the camera was made for. And I think it would be a shame to get rid of it ust because the video mode doesn't work right. I think you should keep it for still photos and take a look at real DV cameras. You'll have to spend more, but you'll have the right tool for the job.