If you open the car with the key in the door does it set off the alarm? If not, can the key still be used to start the engine?
Edit for further info, it looks as though you can re-sync the plip this way:
1) Get in the car and shut the door
2) Put the key in the ignition and turn it to ACC (the position before engine start)
3) Within 10 seconds of putting the key in, press and hold the lock button on the fob for 10 seconds
4) Remove the key and release the button, get out the car
5) Press the lock button on the fob