It only works with the ignition off, did you have the ignition on when you pressed it? The boot opens by a solenoid. The power to it is cut when the ignition on so that bored passengers don't go pressing it and opening your boot on the move!
The solenoid is behind the lock on the inside of the tailgate. Remove the plastic trim - be careful levering off the trim, the clips tend to break. Check the wiring connection to the solenoid. You can't fail to miss the sound of it when it's working, it's a very loud click / clunk!
If that's ok, then do you know if someone has had the centre console / ashtray out? Just a simple idea to start with, maybe the plug isn't connected properly at the back of the switch.
If it turns out to be the switch or the solenoid that's failed, I have them from my old car if you need one.
My bet is a wiring plug. It could be as simple as it not being re-connected after someone replacing the dash lights or something.