Elusive Tube-Amp Hum

This is my first post here, thank you for having me.
I'll try to keep this quick. Please excuse lower than average technical grasp.

For those who like puzzlers:

I have an Antique Sound Lab DT1001 which is a chinese manufactured integrated 50w/pentode zero-feedback unit with separate power, L&R output and choke transformers & 7AU preamp and KT88 power tubes.

I have had it for a year after buying it, marked down, with "cosmetic defect" from Audio Advisor.
From the start it has been a lemon for one single reason but I have kept it because of the amazing sound.
The problem is that a "60 Hz hum" will suddenly occur at any given moment and steps need be taken immediately to stop the hum. This symprom presents itself usually once only in every duty cycle/listening session.
There has never been a single commonality in occasions of the hum - it is utterly random.
It is always the same in both speakers and the same volume as the volume setting. One could call it a hum or a buzz. It sounds like an electric guitar pulled out from an amp. It makes me run to turn the unit off. The hum can occur when the unit is warming and no program is playing or it can hum the first time after 3 hours of playing music. Music can still be heard under the hum at diminished volume behind the hum.

It happens every listening session. It only happens once per listening session. (this is why I can manage to live with it).

I use only CD source - hum has occured with different players, interconnects, power sources, grounding scenarios and polarity scenarios.
I have switched everything that can be switched, (tubes) and taken it in (non-warranty) for review, touch-up and 3 days of play - at the shop the hum never occured.
The only thing different was the shop didn't take my interconnects. Which made me think.

So, when the hum occurs, I have been playing with the interconnects while leaving the amp on at reduced level. I think the problems - or some strong symptoms, lie here.
As I slip the interconnects (on the back of the amp, NOT the back of the CD player) around and on and off, I can get the hum to come and go, increase or decrease in intensity but never change from (what I believe is) 60hz.
Usually to get past this all by turning it off, letting it sit 10 min and starting over.

If you got this far I thank you for your attention and would appreciate you thoughts or questions,
If you unplug the interconnect completely, does it still hum? If it doesn't, the problem is most likely a lose ground shield in your interconnect.
I would recommend that you have someone skilled in soldering re-solder the connectors, in the amp, to be sure you are not being subjected to a cold solder joint. The symptoms you describe are typical of this elusive beast. Even looking at the joints cannot tell you if they are not well connected or soldered. Best way is to remove all existing, re-strip and clean connections, get to new wire if you can, and re-solder. Be sure to very tightly crimp the wire to the connector, solder is there to seal and insure great connection, not to be the medium.

best wishes
As Mr L mentioned; the problem could be a cold solder joint on a ground connection, or a loose ground terminal on one of the RCA jacks. That the problem didn't occur at the shop, without your interconnects, does make them suspect as well. Cheaper RCA connectors can easily lose their grip at the ground. You don't mention much about yours, other than that you can vary the problem by manipulating them. Does the hum affect both channels? If not; interchange the cables, channel for channel, and see if the hum follows.
Re soldering all the connections from the RCA's inputs is the
first choice, grounds especially, then if not solved, the second choice is the filter capacitors in the power supply feeding the preamp-driver stage.Those could have a bad solder joint too.If its not a bad solder joint, then the electrolytic (caps) for the preamp stage might be bad.Its probably not in the output stage because it would most likely hum all the time,whether the volume is low or loud.Preamp stage most likely.
If you or your friends aren't good at doing this,a dealer in
your area shouldn't have any problems,unless they don't work
on tube amps.Then try a guitar amp tech.They should have tube
amp skills,or tell you otherwise.
If you don't know how to check and discharge the HIGH VOLTAGES
keep out. The caps could stay charged like a high voltage battery for many hours. Turning the amp off while the music is playing (you'll here the sound fad out)sometimes helps.If
you don't know how to discharge the high voltages be warned,and don't sue me,or haunt me if something goes wrong.
You say you are only using cd as source. Assuming the amp has more than one line input, try hooking your cdp to an aux input. If the problem does not present itself the issue is most likely the cd input connectors. If problem persists, there is most likely a problem with the amp as you have stated ICs have been swapped.
Easy, wiggle every interconnect at the junction and every tube, possibly a bad socket, cold solder joint, or cold solder joint in the IC. Every problem has a solution....
Thank you all for your answers, particularly since I am not skilled in soldering or circuit design, I now can describe to my guitar amp tech (who I know at a local store) where to start checking for issues.
We hope you get back to enjoying your music!