Check that the timing IC works.
You may have to swap the capacitor C1.
It looks like that the timing oscillator doesn't start hence the continuous alarm.
I don't think the piezo buzzer will reliably work of such a low voltage. It might work with new 3V batteries but once the batteries have discharged to about 2.4V the piezo will only get 1.8V as it's being powered from an emitter follower.