What is the resistance of the buzzer?
Write a simple sketch that toggles the pin with the buzzer, to see if things work.
Try:
if(TimeHours10s == AlarmHours10s && TimeHours1s == AlarmHours1s && TimeMinutes10s == AlarmMinutes10s && TimeMinutes1s == AlarmMinutes1s )
{
Serial.print("Buzzzzz"); // set up Serial.begin(9600) in setup()
digitalWrite(Buzzer, HIGH);
delay(100);