The alarm module is a state machine.....
So without proper initialization (you hear the power on beep sequence), preforming those(any) tests with it will give false negatives.
i.e., The module will remain forever in its first state (NOT BROKE) until you get it to initialize properly.......It has to see expected value/s upon power up to go into its next/final state of functional else...STOP!!.
Doing any testing with it and making conclusions on how it did or did not react without FIRST hearing the power up beep sequence is pointless, it's not getting to that state.
No power up beeping means simply three things........
1) Beeper bad (checked)
Moving on........
2) Module bad (he's swapped one out already).........
Moving on........
3)Sensor level bad (bad/broken sensor, connectivity, supply voltage)
We're here now, checking things off the list.....Not so complicated? For even for "simple people"?