OK. I have a Technics SL-D1 plugged in to a new pre-amp plugged in to a new, basic Sherwood receiver. The record player has its built-in grounding wire attached to a random screw. The buzzing is still pretty audible, if not deafening. It's definitely annoying, and affects the sound while records are playing. No other component has a buzzing. We've heard you can plug the record player in to a different outlet than the receiver, and that might help, but we don't have another outlet in the room. Any suggestions?
A "random screw" is not a good grounding point. Not all screws are going to provide a chassis ground. Make certain the screw you connect to is not insulated by paint on it or the chassis and try another screw position if you do not have a dedicated phono ground.
Additionally, all of the audio input jacks on the back of the receiver are connected to chassis ground. With the volume control turned down touch the bare wire of the phono set up to the outside of one of the unused jacks. If this lowers the noise, you have to find a good chassis ground point.