Everything your TV does -- how it displays images, how it handles operations of its buttons and remote, how it gets power from the wall, etc. -- can be explained in terms of the physical parts and the information stored in and travelling through it, without exception.
Most likely, your TV contains a sealed cathode ray tube. Suppose I were to posit that there's some invisible, indetectable component inside the cathode ray tube. You can't ever see it because the moment you break the cathode ray tube, it escapes. You can't detect it because it exists in a way that is beyond the ability of any of our instruments to detect (though any time something unusual happens with your TV that isn't immediately explicable, I might blame it on this mysterious, ethereal component).
If you ask me what this component does, I will vaguely intimate that it influences the nature of the shows you see. If it were absent or corrupted, the shows would be different, lacking in some quintessential element or altered in some hard-to-pin-down way. "But the show comes from the satellite dish, it's the same for everyone," you dispute, to which I reply with a sagacious air, "No, it varies; some people see it darker, or redder, or with differences in sound." "But those," you retort, "are explicable with differences in the hardware and settings!" With an air of unwarranted confidence, I respond claiming that this ethereal component has an undefinable influence on these things, which cannot be measured.
Years ago, people universally insisted it was this component which decided what the picture looked like, but later examination of TVs revealed how the signal and the action of the cathode ray tube and the phosphors causes the picture, though a lot of people still can't get their head around this -- they have problem with the idea of a complete, moving, colorful picture that conveys meaning arising from the repetition (thousands of times each second) of so simple an action as firing a cathode ray at a cluster of three phosphors. Secretly, these people suspect that, while all that might be necessary, it's this ethereal component that causes the result to form an actual moving image rather than a pattern of shifting colored dots.
There are some people who insist that when your TV breaks down and you get a new one, this component "transmigrates" from the old TV to the new one. There are sometimes fierce arguments between those and the ones who insist that when the TV breaks down, this component finds its way into a huge combination plasma/projection system on another planet, where it gets to display only the best shows. Despite the depths of this dispute, both sides take the attitude that this component is what makes your TV the specific, unique TV it is, what distinguishes it from every other TV in the world.
The most noteworthy point you raise, though, is that there is not one single thing which we can detect which is explained by this component. Everything your TV does can be explained 100% by the interaction of hardware and information, even if you, personally, don't fully understand every detail of all the components and their actions. Yet I insist there's some extra component which cannot be detected, serves no definable purpose (apart from covering up my failure to understand emergence), and which is primarily a sort of "ID tag", a component which gives the whole system a unique identity that in turn has no measurable effect.
Silly, huh? And yet most people believe the exact same thing about your body and mind.
Okay, to be fair, I know that some people ascribe specific characteristics to souls, and the question of what can be "proven" to be attributable to them is still hotly contested; and there are any number of poorly understood things that could be, when better understood, caused by some as-yet-unknown process that gets the name "soul" slapped onto it because we already have it lying around.
However, I think that the majority of Americans, when they refer to a soul, are doing one of two things. Either they're referring to an actual "thing" which doesn't seem to do anything, and to which they attribute a lot of patterns of behavior that are actually perfectly explicable by physical means that they simply aren't aware or, don't understand, or refuse to believe; or they're referring to something so vague, such a "hyperextended rice pudding", that you can't pin it down enough to evaluate its truth or falsehood, and in the end, they will probably turn out to be referring to nothing more than emergence itself. (Though they'll probably refuse to conclude, in this case, that patterns of traffic on highways, or prices in the stock market, or the flocking of birds, each possess a soul.)
Ultimately, I think the concept of a soul is a holdover from a time when we didn't understand very well how the behavior of body and mind emerge from physical things (where hardware and information meet); it is a vestigial concept we haven't divested ourselves of simply because so many people are so ignorant of so much.