A fuzzy photo without any light is useless.
A capacitor marked 473 is 47nF.
Disconnect everything from pin 2 of the 555 except the 10k resisitor to the positive supply, the 47nF capacitor and the other 10k resistor to the positive supply at the other end of the capacitor. Ground the input for a moment like this:
The 555 should get triggered, the buzzer should sound for the timing then stop when the 555 times out.
1.1 x 10uF x 1M= 11 seconds with the pot at max resistance. They show a graph that looks like 8 seconds.
The 10uF capacitor could be actually only 8uF or 12uF and the 1M pot could be only 800k or 1.2M so the time will be somewhere from 7 seconds max to 16 seconds max.
Since you replaced the capacitor and made certain its polarity is correct then either the 555 is bad or the pot doesn't conduct.
Before buying another 555 try a 1M resistor to replace the pot.
Measure the output voltage at pin 3 of the 555. With a 9V supply it will go high to about +7.5V to turn on the transistor that drives the buzzer.
Then after about 12 seconds its output will go low to about 0.1V which turns off the transistor.
Maybe the transistor is wired incorrectly or is shorted.
Your transistor's pins are correct.
Didn't you solder the circuit together? Or is it on a breadboard that has intermittent contacts?
Make sure that pin 6 of the 555 is connected to the 10uF capacitor and 1M resistor.
Make sure that the 1M resistor connects to the positive supply.
What kind of buzzer? A mechanical one has a coil that creates high voltage spikes that needs a diode across it to stop the spikes from destroying parts in the circuit.
The new circuit you attached has the transistor connecting pin 2 of the 555 to ground when it is dark. The 555 does not time out when its pin 2 is low.
That is why I added a resistor to make pin 2 high and a coupling capacitor to pulse pin 2 low for a moment.
You forgot to join pin 6 with pin 7.
Post a pic of my circuit on the breadboad.
The left buzzer is a piezo beeper. I don't know what is inside the right one.
Connect another transistor, LDR and 100k pot in the same manner as is shown in the diagram and connect the collector of the second transistor to the collector of the first.
Thus if one or the other LDR is in the dark, the associated transistor will be turned on.
By the way, I notice that you now have the buzzer connected to the 555 output without Q3 - as I suggest previously.
I don't think the new circuit will time out when it gets dark. The datasheet for the 555 says that pin 2 must be high for it to time out. The transistor holds pin 2 low when it is dark.
I think a coupling capacitor and resistor are needed at pin 2 like this: