As mentioned in post #9, "If the serial monitor showed nothing, you also have a problem with the code."
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Check your buzzer's functionality by writing a very simple, couple line sketch.
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To more easily chase your problem, change this line of code to one item:
if(TimeHours10s == AlarmHours10s && TimeHours1s == AlarmHours1s && TimeMinutes10s == AlarmMinutes10s && TimeMinutes1s == AlarmMinutes1s ) -
To prove variables are what they should be, you can add some diagnostic lines of code at strategic locations, Serial.println(AlarmMinutes1s); .