Unless you are connecting the table to a unit with a DIN input you do not need to put back the DIN cable. While that is a cheap RCA cable it is one that B&O used on later 4004s and many others. If the hum does not change when using the ground wire to your phono inputs it’s likely that it’s not properly grounded internally. I have replaced many of these and it needs to be done correctly since the DIN cable has a double shield system. Are you comfortable with soldering? If not a competent tech can do this but I would simply use a higher quality RCA cable.