Then I missed the part where you switched speakers and the problem stayed in that channel.

Switch the speaker wires at the receiver and test again. You didn't say if the speaker wires are in the wall or not.

Hum or buzz is there when speakers unhooked from amp. Rules out the amp...
must be hum inducted from running the speaker wiring in paralell with A.C. lines?

The amp in the one speaker has a problem- the noise moved with the speaker when he swapped the left with the right, so it's not induced noise.
 

To the OP- move the noisy speaker to another room and plug it in- if it still makes noise, the amp has a bad ground, cap, whatever. Move it back and connect it to the system with the power cords plugged in and listen to the response with full-range music. Connect the sub out from the receiver to the speakers and listen for the bass to improve- if it does, you need to address the bad power supply/amp issue. Unplug the power cords or turn the amplifiers off and if it doesn't make a difference in the sound, leave them unplugged. If the customer likes more bass and wants that for their system, either have the power supply/amp repaired or sell them new speakers and a subwoofer.

Geg everyone out and burn down the house.

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Then there is this

Exactly!
This points to the amp channel or inductance!
Try running a new wire to the left side. If this doesn't work you are looking at an amp issue. If it does then you are looking at inductance.

DOH! I should have gone back and re-read the part that says the problem stayed at that side.

I would go to the basement and look for the bundle of Romex that goes up to the second floor (if there is a second floor) through the wall. If that, or the breaker panel, is directly behind/below the speaker, it could definitely cause problems. I would also move the speaker away from the wall, to find out if the level of hum/buzz decreases. That would be an immediate indicator.

Wow, thanks for all of the input! To clarify a couple of things
-the sound is only from the left front channel, no matter which speaker is connected there. This means that the issue likely doesn't have to do with a specific speaker;
-the sound only starts once the speaker has sound fed to it;
-the sound stays if you unplug the speaker-level inputs to it and only goes away when you unplug the speaker from the outlet. This means that the issue isn't the receiver.
-the sound is still there if you run an extension cord to the speaker so that both speakers are powered by the outlet from the right front channel. Doesn't this mean that the issue isn't the power?


I'm leaning toward this!

CJ

Most amplifiers in speakers and subs are a bit less than amazing but for the sake of symmetry, it may be worth repairing, if that's where the problem lives.

Edited to add- if you have a spare speaker-it doesn't matter if it's an in-wall or not, connect it to the speaker wire on the left channel. If you hear hum, it's the receiver or induction/another problem. If it hums, .try using a different speaker wire AND speaker. If the wires were fished in the walls, try a different piece of wire and if the noise stops, you'll need to use a new wire. If you don't hear noise, swap the right and left speaker wires at the receiver. If the noise stays on that channel, induction/coupling is likely. Measure the resistance from the left speaker wire to the ground at the nearest outlet. If it's continuous at all, someone killed the wire and it needs to be replaced. I posted that you might want to move the speaker away from the wall- do that with and without using a different speaker wire.

Leaving the left speaker on the left side plug it into the right output.

Do the same with the right to left.

If the hum switches sides its the amp. If it does not switch sides its the wire.

Run a new wire across the floor and see what happens.

He says it stays when he removes the speaker wire from the amp with the speaker plugged into AC, thus removing the speaker wire from the equation. This makes me believe that it is related to the amplifier within the speaker.

He also wrote that he swapped the speakers' positions and the problem stays on the left side, so it's not the speaker's sub amp ao, if anything, the receiver might not like seeing these speakers as the load or, in a rare case, something is inducing the noise into the speaker wire. It usually happens on low-level signal-carrying cabling that terminates into/from high impedance circuits.

To the OP- are the speaker wires bundled with other cables and power cords?

I may have missed it but do you have both the speaker level inputs and low level inputs connected? Is there a switch on the built in amp that allows you to choose which input you are using?