Hum and buzz is the single most frustrating problem with systems! Patience and persistence seems to be the best answer there is; experience helps (hence the Forum) but not as much as you might hope.
The signal ground starts at the ground plane which is electrically connected to the chassis plate at the ground post. The power line safety ground is connected to the chassis plate near the IEC socket - that's how the two are connected.
When touching things helps, it is quite possible that the interference is radio frequency pickup. For example, perhaps the CD player has a switch-mode power supply which is not well shielded, or which radiates from its power cord (poor line shielding). Or something else - a light dimmer, flourescent lights, battery vibrator in an adjacent apartment (no kidding, it's happened). Another source used to be television signals, with its 59.94Hz vertical refresh rate. The usual answer is shielding, such as the tube shields and a metal box around the circuitry - the chassis is drilled for it. I can't put my hands on it but there must be a thread or two - can someone find it?
Shielding acts on electric fields by surrounding the circuitry with a metal container which is grounded, draining any induced field to ground. That's one of the reasons I wanted to start the search for causes by making sure all the grounds were in place. Normally I would expect that if the chassis is well grounded, then touching it will just drain whatever your body picks up to ground, and will not have an effect. So I think the jury is still out on what is the real cause of what you are hearing.
