Why is my radio circuit not functioning correctly?
I'm not sure where this circuit originally came from, but a quick google search for "transistor radio circuit" produces it as a first result from Wikimedia Commons.  

Unfortunately, as some of the other folks commented, this circuit won't work.  Here are some details on what's wrong with this circuit:


The antenna wire connected to the parallel LC circuit provides a tunable LC resonator, but the signal received and converted into a voltage across the LC network is a small AC signal.  It does not have high enough magnitude to drive the base of the BJT on its own.  You need to add a DC bias network to this circuit to properly bias the BJT in forward active mode.  The small signal from the antenna should then be AC-coupled to the BJT base.
The signal from the antenna should be demodulated before being amplified to extract only the audio signal and remove the higher frequency carrier.
The placement of C2 does not make any sense.  Under AC small signal considerations, C2 is an impedance connecting the collector to ground, and large values of C2 could effectively become a small signal bypass short circuit to ground.  Whoever designed this circuit might have been trying to low-pass filter the DC power supply from the battery, but in its current position, C2 does not make any sense.


Instead of designing a circuit for you here, I'm going to use the circuit from Peter Vis' website (https://www.petervis.com/Radios/one-transistor-radio/one-transistor-radio.html), which I found through a quick google search for single-transistor simple radio circuits.  This is a good introductory circuit that demonstrates all the concepts that I just talked about.  Of course depending on the requirements of your application, you may need to adjust this basic circuit or consider other designs, but this should give a fairly good overview.

Here's the circuit from his website.



On the left side, one can see the LC resonant circuit and antenna.  The diode \$ D \$ demodulates the input small signal from the antenna only passing through the lower audio frequency that you want to amplify and ultimately hear.  

The amplifier used here is a very simple NPN BJT common-emitter amplifier stage.  If we look at only the DC bias point (only the battery, transistor, and resistors, without the AC signal from the antenna), we can see that the collector and base are both fed through a series of resistors which carefully establish the transistor in forward-active mode.  There are several considerations that need to be made when designing a BJT network for forward-active operation, but for an introductory application such as yours, I'll summarize them as follows:


The base-emitter junction needs to be forward-biased (i.e. the base voltage needs to be higher than the emitter voltage, which in this case is ground).
The base-collector junction needs to be reverse-biased (i.e. the collector has to sit at a higher voltage with respect to the base)


As I mentioned before, there are more considerations you need to take into account when designing the DC network to bias your amplifier: base and collector currents and collector-emitter saturation voltages to name a few.  All of these design considerations can be found in introductory microelectronics textbooks or courses.  

Now, to amplify the signal incoming from the antenna-resonator network, we want to first inject the small AC oscillations that comprise this signal onto the DC bias point that we have just described.  The AC coupling capacitor connected to the diode accomplishes this.  

The AC small signal voltage is fed to the base of the common-emitter stage and is turned into an amplified current version which then passes through the speaker.  The degree of amplification depends on many factors such as the choice of BJT, the DC bias points, and the speaker impedance.  The important point here is that the transistor acts as a transconductance, taking in a small voltage oscillation and converting it into an amplified current output.

Amplifier and RF electronics design are a whole field of study and design, and there are many changes that can be made to this simple amplifier circuit to improve its performance from different perspectives.  This is a good starting point for a beginner, along with either taking a course in or reading a textbook about analog circuit design.