Hi. Basing myself on the datasheet and the pictures, I have appended my take on the schematic below.
C1 must go to the C pin of the SAB0600, since you need it to set the frequency of the oscillator. The suggested value of 4.7nF seems good enough; together with the 15K resistor should give a frequency near enough to the 13.2KHz suggested by the datasheet.
C2 should go to the Q pin: test the continuity with a voltmeter. If it does, I would use the suggested value of 330nF. The L pin can be left floating: the output of the IC will be a square wave, which sounds rather worse than a sinewave; it seems the manufacturers made that trade-off.
C3 looks like a RC timer together with the 100K resistor. When green goes low, the Vs node goes up in voltage, and it pulls up pin E through the capacitor. That resets the IC for the duration of the RC delay. I would leave this cap in place unless you are quite sure it is blown. If it is, you'll have to guess the delay time, and infer the capacitance from there.
In order to test the circuit, first of all I would test all the diodes and the transistor with a multimeter. If they work, I would consider replacing both polarized caps for equivalents; the yellow one is clearly a tantalum. Respect its 25V rating. Or you can directly try powering the circuit up: get yourself a 12V supply, and connect black to ground, and blue and yellow (and green) to 12V. Note that the IC has a maximum tolerance of 11V, but there are two diode drops, plus the transistor and the 100Ohm and 47Ohm resistor, plus the zener, which probably is around 9V. So a 12V supply should be OK, and is typical for a car battery. Connect the green cable to 12V too, to keep the switch open for now, and test the zener for its voltage. If the voltage in the zener is about 11V, it is there as a protection for overvoltage. If the zener voltage is under 11V but over 7.5V or so, it is there for regulation, and it is working. If the voltage at the zener is under 7V, it is failing and does not give voltage enough for IC operation: replace it for a 9V or more zener, and try again. Now switch the green cable to ground, and wait for a chime. If the circuit chimes, it is working, and the problem is either solved, or elsewhere in the car. If the circuit doesn't chime, there is something wrong: the IC, the speaker, some cap, whatever. To test the IC, watch the Q (sound output) with a 'scope after switching, you should see the chime. If you don't, watch the E pin for the RC decay after switching: if you don't see it, C3 is suspect. If C3 works but the IC doesn't, either the IC is blown, or C1 is failing, and there is not oscillation. If you see the sound waveform but hear nothing, either C2, the 10u cap, or the speaker are blown. If during testing you see the smoke come out, you have your work done for you.
And so on. I hope this helps.