Where does background noise go on a radio station? If you tune a radio to a frequency where there is no station broadcasting, you hear noise.  It's pretty loud, just as loud as the music that comes in when you find a station.  And yet, when you do find a station and you have good reception, the music that comes in is crystal clear; it's not mixed with noise that's just as loud as the music.
Even more strangely, several years ago (before the advent of HD radio and digital transmission) the radio station I usually listened to was offline for a day due to technical issues.  When I tuned to the station that day, I heard nothing, not even static.
Where does all the noise go when there's a station transmitting on that frequency?
 A: The "noise" you are hearing is an artifact of no carrier signal being received. A carrier signal is the waveform on which the audio is transmitted - example AM and FM are both forms of carrier signals. 
http://en.wikipedia.org/wiki/Carrier_signal
When your radio receiving device isn't receiving a carrier signal, its audio output will sound "noisy" because of naturally occurring radio frequency noise - which is result of many things like the sun. That is to say, there are many things in nature that emit random radio frequency waves! A radio transmitter must use enough power to overcome this natural "noise floor". If your radio receiving device is within a distance close enough that the power from the transmitter overcomes the natural noise floor, it will output that signal. Otherwise it will output the naturally occurring noise. 
The three states indicated in your question are: 
1) Noise (aka static) - which occurs when no carrier signal is being transmitted. 
2) Silence - which occurs when a carrier signal is being transmitted, but no actual audio is being sent over that signal.
3) Normal Audio - which occurs when audio is being transmitted over a carrier signal. 
So in your example, the station's audio wasn't working, but the carrier signal was being transmitted. This likely occurred because there was an issue between the DJ booth and the transmission tower. For example, the audio link between the radio station's audio mixer and the transmission tower may have been cut. 
A: The answers to the last question we've had about radios suggest we have some experienced radio buffs around, so regard this answer as provisional until someone more experienced replies.
Anyhow, radios generally automatically adjust the gain of a received carrier signal. This is so that weakly received stations are as loud as strongly received ones. When there is no signal at all the radio will increase the gain to the maximum to try and pull in a signal, but all that gets amplified is the noise. The noise will have about the same loudness as a station with good reception (though the ear tends to perceive the noise as louder). When a strong station is being received the noise is still there, but since the gain is much lower the volume of the noise is much lower. You could probably hear the noise during quiet moments in the transmission.
To avoid the unpleasantly loud noise, many radios will automatically mute the volume if they can't detect a signal. So whether a detuned radio produces noise or silence depends on the design of the radio rather than any fundamental physics.
I should add that in the particular case of the radio station being offline, the station may have been transmitting a carrier signal but with no modulation. This would also be almost silent, though if you turn the volume up you should be able to hear some background noise.
A: For FM radio, the information is carried in the frequency of the signal and not in its amplitude.  This makes gain control a lot easier.  One common technique is the use of a limiting amplifier on the RF input.  A limiting amplifier will add a very large amount of gain, so much so that it clips off the top and bottom portion of the waveform and only keeps the zero crossings.  The resulting signal is then FM demodulated.  So long as there is a strong carrier, the positions of the zero crossings will not be disturbed and there will be very little noise at the output of the demodulator.  However, when no carrier is present, the noise present at the input of the limiting amplifier will be amplified and will produce significant noise at the output of the demodulator.  
