Being able to hear the radio tuner while the RCA cables are unplugged seems to indicate inductive noise or a ground loop.

Make sure there is nothing loose rattling around inside the player.

Check the sled wiring for loose crimps.

Check: Every. Single. Wire. Between the player, its power source, the amp, its power source, etc., and triple check every single ground wire. Open the player and make sure none of its wiring harnesses have come loose or are chafing inside anywhere.

Look here and here for the starting point for noise and ground loop troubleshooting.

Make sure you've adjusted your amplifier input gains down, as described here in the section titled "Properly adjust the input gain level on the amplifier(s):"