Shooting Sports in a Cafeteria

I am a yearbook advisor that is forced to shoot sports in a cafeteria with terrible lighting. I have a 60D with a Sigma 70-20mm f/2.8 and a Sigma 24-70mm f/2.8. The 70-200mm is almost too long to take pictures in the tiny cafeteria, especially with the crop factor. I have been shooting in aperture priority at f/2.8, but in order to get a shutter speed fast enough I have to set the ISO at the highest setting and the pictures get really grainy. In shutter priority if I set the speed for 1/500 the pictures are really dark. The only thing that I have been able to do is shoot in aperture priority at f/2.8 and set the ISO at 3200 and get a slow shutter speed of 1/250 or 1/125 or even slower. That does not freeze the action when shooting basketball. If you can tell me anything that would be helpful it would be much appreciated.