Why is my oscillator circuit not working?
As far as I can see on the photo the circuit seems OK, except


the capacitor is the wrong way round: the white strip identifies the negative pin.
I can't verify whether the LED is the right way round. Bridge the left LED pin to the + with a 470 .. 4k7 resistor, if it lights up it is OK.
you don't show the power connection. Be aware that some solderless breadboards have a break in the middle of the power strips.