You may want to do as our resident expert Sport Shooter Homer does and go to AV mode and shoot wide open, This will force your camera to shoot at the highest shutter speed availeable for the light..
Were all of your shots when you shot in TV mode at full open aperture? Why I ask this is because of whta happens whan you shootv on ICE or snow...Because of all the White and the way the meter works, you may be getting underxeposed images and underexposure leads to more noise then high ISO does. So if your camaera was actually underexposing the shot, that may be the source of your noise.
You may want to try using Exposure compensation ( look it up in your manual if you don't already know how) and give it a boost of +1 stop. This may help the exposure and your noise Issues
A faster lens such as the 70-2002.8 would be nice, but if you can't afford that one, and you can get close enough to the action you may want to try a lens like the 50mm 1.4 or the 85mm 1.8 to give you just a little more light into the camera.
Good luck, sports indoors under lights is tough!