How can I take sports action pictures at night with Canon S3 IS camera

On sports mode-too much noise
On any other setting it takes too long for flash to go off and I miss the action. I tried taking picture without flash but it's too blurry.

Taking action shots in general is difficult to master. Taking action shots in very low-light is even more impossible. In order for a camera to incorporate enough light into a picture, the shutter needs to remain open much longer. In an action shot, when shutter speeds need to be as high as possible, long shutter speeds just aren't acceptable. If your subject is more than 10-15 feet away from you and you use a flash, the light likely wouldn't be strong enough to increase the shutter speed enough to take a non-blurry picture. As a compromise, the camera will increase the ISO sensitivity to improve light performance. And that's what causes the noise.

I'm afraid there's not much you can do about this issue. I believe there is an external slave flash for the S3IS you could purchase that would double the intensity of the flash, possibly allowing you to produce higher shutter speed shots at lower ISOs that would alleviate your problems. But as it stands, you're always going to have a difficult time with low-light action.

yes i had that same problem shooting snowboarding action shot. blurry shots or bad noise most of the time.try full auto and fix iso to match scene.