You will probably ned to get the shutter speed up to 1/250 sec. to freeze action. Can you shoot wide open and/or raise the iso?
I have shot ballet where flash was not permitted, my iso was 1600-3200 to stop the movement.
Turn off the digital zoom and crop on the easel; see if that is not an improvement as well.

That is a very tough shooting situation. As Ronk points out you'd need the highest ISO possible, which I think is 800 on that camera. Only a few DSLRs do better; some film can handle 3200 without major trouble. With the zoom at its optical tele end (Ronk is also right there) you will not have a very fast aperture. In some ways you don't want it because the distance away creates some decent depth of field but the tele takes it away and in low light your camera will have some focusing challenges. One possibility is to accept a fairly slow shutter speed and pan with action; there will be body parts that blur and the background will blur but this might make for an interesting effect.

Actually I disagree on the highest ISO because you're sitting in the dark, not your subject. I think the problem stems from not using the right equipment for the type of photographs you want to capture. If you set your zoom at the widest angle, it will open the variable aperature to the largest f-stop and you might have to walk down to the edge of the ring and shoot because you'll be using a wide angle lens. But you'll also be able to shoot at a faster shutter speed and capture action at an ISO that will give you a higher quality image.

I agree with Larry on getting closer and using a wide angle. I do think the question of ISO can be a bit more contextual than "go high" (my suggestion) or "go lower" (for quality; Larry's suggestion - I doubt he'd disagree with this though). I think it depends on a number of factors, one of which is (as he notes) how bright the subject is. When I shoot indoor basketball (up close) I don't find it all that bright. Not considering the other factors in favor of a high ISO, which are the need for a fairly fast shutter speed and some depth of field and hence some stopping down of the lens. As Larry notes there is also the issue of image quality, which I think depends on the purpose of the shot. Let's say your camera has very low noise and the right exposure at ISO 200, but you'd be better off stopping down twice and quadupling the shutter speed (not so unlikely) you are looking at 3200 which will either be impossible or a bad image quality. So you are faced with a challenging shooting situation. These were my assumptions about your case, which I now see are wrong. Your lens really has a focal range of about 7-51mm, so at "200mm" you're really 51. At the distance you've been at you've got lots of DOF even wide open at f/3.5 (the widest at that length). If you go close at 7mm or so you'd have to get in the ring and shoot a belly button to have DOF issues. I looked your camera up on:
www.dofmaster.com/dofjs.html which is one of the nicer DOF calcuators on the web. It does have your camera. You'll see that after distance to the subject, the main factors are aperture and focal length, but it's also interesting to see the influence of image (sensor, negative) size as well. (Your camera has less DOF at 51mm than a 35mm camera at 51mm, but of course it has a great deal more than the 35mm does at 200mm.) To make fair comparisons across camera systems, then, you have to take into account the aperture that each camera can handle because of noise/grain performance at high ISOs; this was the reason for my reference to film, because films like Kodak 400CN can be pushed to 1600 and even 3200 without much trouble, which can give the edge to older film cameras unless you have the most high end digital equipment.