How can we discern so many different simultaneous sounds, when we can only hear one frequency at a time? As I understand it, the eardrum works like any other kind of speaker in that it has a diaphragm which vibrates to encode incoming motion into something the inner ear translate to sound. It's just a drum that moves back and forth, so it can only move at one rate or frequency at any given time.
But humans have very discerning ears and can simultaneously tell what instruments are playing at the same time in a song, what the notes in the chord of one of those instruments is, even the background noise from the radiator. All of this we can pick apart at the same time despite that all of these things are making different frequencies.
I know that all of these vibrations in the air get added up in a Fourier Series and that is what the ear receives, one wave that is a combination of all of these different waves. But that still means the ear is only moving at one frequency at any given time and, in my mind, that suggests that we should only be able to hear one sound at any given time, and most of the time it would sound like some garbled square wave of 30 different frequencies.
How can we hear all these different frequencies when we can only sense one frequency?
 A: 
But that still means the ear is only moving at one frequency at any given time

No, it doesn't mean that at all.
It means the eardrum is moving with a waveform that is a superposition of all the frequencies in the sound-wave it is receiving.
Then, within the inner ear, hair cells detect the different frequencies separately. It is entirely possible for several hair cells to be stimulated simultaneously so that you hear several frequencies at the same time.
A: 
So too much frequency and you do lose the ability to decipher it and it starts to just sound like nosie?

If that happens, it's because of how your brain interprets the signals that it receives from your ears, and not because of the physics of how your ears work. If the total sound pressure level is not so great as to damage your hearing, then your ears will faithfully report all of the frequency components to your brain, but there seem to be limits to how many distinct "signals" your brain is able to derive from that information at the same time.
A: As you mentioned, all the different waves get added together in a Fourier series.
The hair cells in the inner ear are essentially performing a Fourier analysis of this combined wave, splitting it back into its component frequencies. The amplitudes of each frequency are then sent to the brain, which performs higher level analysis to recognize specific types of sounds (and also determines the direction of the sound sources by comparing the timing from each ear).
A: The human ear doesn't hear one frequency at a time.
A way to physically see what the ear is experiencing is to take a pool of water.  Now make some waves.  Splash around.  See how the entire tub gets full of up and down motion all over the place?
In the air, similar things happen; but instead of "up and down" those waves correspond to changes in pressure.  (Air is much more compressible than water; water will expand upwards a whole bunch under a pressure wave, while air will mostly just compress).
Now stick a small toy in the water as you splash about.  See how it floats up and down?
Build two mesh tubes.  In those mesh tubes, place a float.  Have them free to float up and down with the waves.  Now splash around.  The movement of those floats in the tubes is basically what it is our ears are detecting.
With that simple signal, our ears and brain can determine that there are 3 waves in the bathtub, and the direction and size and characteristics of each, even though the bathtub is sloshing around like crazy.
To do this, first of all make the "mesh tube" directional: it is now shaped like an rectangle, and only short one side is open to letting waves in.  Add a funnel at the entrance to guide waves in.
Next, instead of one float, have a whole bunch of tiny floats along the oval-shaped ear canal.  Now waves go in, go down the rectangle, bounce off the end, then come back.  Each of the floats independently picks up upwards and downward motion of the waves.
Hook those floats up to a nervous system, which filters and combines the signals from both rectangular tubes.  Then attach that to a brain, which builds a 3d model of where the waves are coming from and what kind of motion each kind of wave has.
Now, a signal of a fixed "pure" frequency in the bath tub causes a certain kind of signal to be picked up by the ears.  But more complex signals are equally handled by this system.
Frequency breakdown is something we do mathematically, partly because it models some of the stuff our ears do.  Signals of a specific frequency (rate of change in the pressure wave) excite certain of the "floats" (actually hairs) in our ear canal, and the math we do to turn a set of pressure changes (sound) into pure frequencies is [b]similar to[/b] part of the system of how our ear canal hairs convert the pressure changes into signals.
Our ears are evolved to pick up such frequencies, because pure frequencies correspond to repeated vibration of some object.  And repeated vibration is something a lot of evolutionary interesting things do; when something partly supported gets an impact, it vibrates for a bit.  That snap of a twig, clatter of a rock, rumble of lungs, rustle of a leaf, or thump of a footstep is very useful to detect other creatures who we might want to eat, or might want to eat us.
So while we hear pure frequencies, we are in effect amplifying their importance out of the jumble of pressure changes our ears are detecting.  The other pressure changes still happen, are still detected, and still go into our brain.
A: The short version: that's not how the ear works.
The eardrum resonates in sympathy with all vibrations in the air, within its physical constraints.
It transmits those vibrations through three small bones (named the "hammer, anvil and stirrup" because of their shapes) into a fluid-filled, spiral-shaped chamber called the cochlea.
The cochlea is is lined with cells from which project very small hairs called "cilia" into this chamber. As the fluid resonates, so do the hairs. Since the hairs vary in length, each one resonates only to a specific narrow range of frequences.
When it resonates, it sends a signal to the brain via the nerve fibre it is connected to. So the brain will receive separate signals which taken together represent the intensity of each individual frequency component.
See https://en.wikipedia.org/wiki/Stereocilia_(inner_ear) for a more detailed explanation of auditory mechanosensing within the cochlea.
A: It depends on what you mean by "at a time". If you mean an exact instant of time, no frequencies can be detected because frequencies are distinguished by how they change over time. However, research has shown that times under around 100 ms are perceived by the human brain as "at the same time". For a 20 kHz signal, that means that there are one thousand cycles per "moment". At the lower end of human hearing of 20 Hz, there are only two cycles per "moment", and at that point we start to perceive vibrations as beats rather than tones.
A comment suggests that you're not quite clear on the concept of Fourier decomposition. The idea of Fourier decomposition is that each frequency is an independent signal, and can be detected completely separately from the others. Each cilia in our ears resonates to a particular frequency. What that means is that over the course of many periods, the frequencies that differ from that one are dampened and only the target one remains.
Consider a swing. If the swing has a period of two seconds, the pushing it every two seconds will make it go higher. Pushing it every one second will cancel out: one push will be when the swing is going the same direction of the push, and so will make the swing go faster, but the other will be when the swing is going the other direction. If you push every half second, then two of the pushes will be when the swing is going the same direction, and two will be opposite. Every frequency faster than once every two second will cancel out. And they will all cancel out separately. If you have a hundred people, each pushing at a different frequency faster than once every two seconds, they will all cancel out. The pushes won't be "so complicated" that they will stop canceling out.
A: the human ear separates out and detects all the frequencies within its range individually (in parallel) in real time, and sends that decomposition to the brain along a bundle of nerves.
The eardrum responds to the instantaneous sum of all the different frequencies impinging upon it. That complex amplitude sum looks like a crazy squiggle which moves the eardrum back and forth, which movements are acoustically transmitted to the cochlea, which then does the frequency decomposition job.
This is entirely analogous to the idea that a loudspeaker cone can simultaneously respond to a complicated mix of many different frequencies and convert them all into sound waves.
