Steve,
If you open up the Beocenter you will see a ground wire running to the middle screw at the bottom of the cassette assembly (nearest the front of the unit). Unscrew the screw and clean the wire contact, I would suggest that you run the wire underneath the metal tape deck assembly rather than sitting it on top and relying on the screw to form the earth to the unit.
I rebuilt my tape and noticed a humming noise from my speakers, I cleaned this wire and relocated it to under the metal surface of the tape deck assembly and then sat the assembly on top of it then replaced the screw, removed the noise totally.
Also worth checking the other end of the ground wire to make sure its attached correctly.
Worth actually poking around the whole unit to check ground wires are attached securely and give them a quick squirt of contact cleaner to ensure they are grounding correctly.
Andrew