Using a MOSFET to turn on a car alarm siren
There are a few reasons why it may not work but as already mentioned you do need a gate to source resistor to discharge the gate and turn the device off when the switch opens: -


Vgs(threshold) might be a little high with the specified mosfet
causing it not to turn on properly. What you can do is try the
circuit with the switch but use the 12V supply for powering the gate
when the switch closes. Don't forget the gate resistor though.
The mosfet is wired incorrectly - check and re-check
The mosfet is damaged - maybe some back-emf from the siren has broken both mosfets - you'll need to put a diode across the siren and use a fresh mosfet.
You are using a different mosfet (easily done so double check)
The 12V power source has become discharged.


My favourite is number 1 so check this out with the switch connected to 12V and don't forget the resistor. However, I'd also put a diode across the siren as mentioned in (3) - anode to mosfet drain, cathode to 12V and make sure it can handle the current of the siren (at least 1A but preferably 3A)