If the noise is in both channels then you should look for something common to both channels. Capacitors are the likely cause, but some IC's might cause it. You say that the volume control doesn't effect it, if that is the pre-amp's volume control then the fault will be after that part.
If your cd player gets older there can be a timing problem by several causes like a slipping belt, or a dirty mode select switch somewhere or a microswitch that is not functional by the slipping belt too long time to take the cd to inside and push up the platter and mechanic to give the focussing of the laser to read the table of contents on the cd , that the cause in 90% microswitch cleaning by contact spray under the tray and on the beginning point wheren the laser begins its start cycle to focussing and give a turning respond to the spindle motor thereis a little microswitch it pushed in or an other switchable point also under or near the cd tray another where the detection is the start that the cd tray is closed and the laser start to focussing on the cd surface and give the cd a turn for the toc and then when its timed correct it recognized and displayed the track position highest priority is that rubber belt that driven the tray and the 2 or 3 microswitches or contacts you should find what have functions in the intake traject. in a short time all together. little suggestion whats meaning Denon DCD815 CD Player disk tray wont open or copy this link https://www.youtube.com/watch?v=H9AbnvF1www
The hum of course is the 60 cycle line AC voltage. Make sure that the routing of the AC power plug is as distant as possible from the stereo RCA cables.
The most likely problem is the connection of the phono cartridge to the wires in the arm. These connections usually are silver plated and become oxidized creating a bad connection. Remove the cartridge and using a fine eraser polish the connections. There is a ground connection that makes the five wire connection. Be super carfull these terminals are very easy to break
The phono connections to the stereo is very low voltage subject to interference. The connection to the magnetic pickup at the tone arm is low impedance and is inductive. Any poor connection between the cartridge up to the AV316 will produce this hum. Continue to check connections and swap cables with a known good to resolve.
I have switched the left and right cables to ensure that the cable is not the problem.
Hope this helps?
If the Nad has pre-amp out sockets that are currently connected to the power amp in the receiver. Then you can sever those link and put the pre-amp out into your Aragon inputs.
Otherwise I don't see how you can connect the amp.