>>I have one dedicated line for power and 1 dedicated line for digital, would you wager a guess as to whether the power supply should be plugged into the digital or power dedicated line ? Thanks.<<<
The power draw of your CD will be a lot less, only a few amps, vs the draw from your from your amp(s). By plugging the CD into the same side as the amp(s) you may find that the heavier draw of the amps may modulate the power supplies in the CD. If your CD doesn't receive enough current, your switching power supplies, dac's, and asychronius clocks will not perform optimumly, also the error correction portion of your CD requires quite abit of current. If the current it requires isn't there, then it can't do it's correction thing properly.
I don't think you want your CD fighting your amp, for the JUICE at the wall.
On the noise issue, Besides balloning RFI into the room, your CD player is also putting back a fair amount of noise into the power supply due to it's normal operation. This would be from your player to it's external power supply
There isn't much you can do between your CD and it's external power supply (it's captive), but your CD's power supply may also be back feeding (adding noise) into your wall outlet. One way to stop this would be to use a Foundation Research LC1 power conditioner/power cord. This is a bidirectional filtering conditioner which is specifically designed to filter incoming on/line noise and back filter digital noises coming out of your CD. I'm not familiar with any other conditioner that backfilters on the backside.
Even with dedicated lines, all grounds and neutrals are bonded at the main panel, so you must eliminate as much of the noise before it has a chance to reenter the circut there.