Allnic H-3000 hum when mute button engaged.

If you're on the West Coast, I agree with others that Albert Porter will probably treat you well. He may even be able to recommend a repair person in your area of California.  Dave Beetles is also a first rate person. And yes, it would seem fair to have the other guy pay for any repairs. By the same token, I doubt he was aware of the problem, which likely is the result of shipping and "handling".

I am lucky in that Bill Thalmann's shop is only about 30 minutes from my house.

Forgot to note that your Shindo stuff is strictly single-ended.  So I don't know whether you can really do true balanced mode, to test the function of the switch.  (I am not even sure how the Allnic achieves balanced output.  It might be via a transformer, since I would bet the circuitry is actually SE.)

Calvin, Do you live on the East Coast, USA?  If so, I can strongly recommend Bill Thalmann in Springfield, VA. Bill is a fine person and smart repair guy who is completely honest.

Speaking of interconnects, can you say more about your other components? Are you running the H3000 in balanced or SE mode? Is the hum in both channels? (I assumed so, since you probably would have mentioned it if the hum was in only one channel.) If you're using the SE outputs, you might try switching to the balanced outputs, or vice-versa.

Sorry for the brevity of my first response to your question about how to open up the case of the H3000. I was typing on my iPhone. I have no idea of your level of knowledge and experience when it comes to working on audio equipment, so that response was based on an assumption that you are not, in fact, experienced. You’ve got a very expensive, very fine piece of gear there. I would not advise you to service it yourself. If, however, you know what you’re doing, you probably by now have figured out how to open the case. Let’s assume that you do find a problem that is as obvious as a loose, unconnected wire. Would you know how to solder it back into place and what it should connect to? If the answers to those two questions are not yes and yes, it would be worthwhile to find a competent tech.

By the way, in my experience, problems like this rarely are as obvious as as a "loose wire". A bad ground could be caused by a cold solder joint that may look fine by inspection.

I don’t agree with Yogiboy, by the way.

No
I've never been near an h3000
you need a pro

Check grounding of the switch inside the unit.  It sounds like engaging the switch causes the Allnic to lose contact with ground.  It should be a simple fix.