@Muppet - Did you replace the battery in the key because the car winds over but won't start? or for some other reason - if so what? Probably won't be relevant but you never know.
And like Dazzler mentioned - do you have a
spear spare you could try?
Also does the immobiliser dash light (car shape with key on top/in it) go out or stay on when you try to start? It should go out soon after they key is successfully recognised - if it isn't it indicates they key isn't being seen/recognised. In an FD model the key needs to be in the ignition - part of this is so a 'coil' built into the ignition can power the RFID chip so as to determine to deactivate the immobiliser. In the GD I believe the process is similar (but the fob no longer needs to be very close to the 'coil'). In an FD the coil has occasionally been known to fail.
FYI the battery only powers the key-less entry aspect of the car (at least in the FD - up to 2012 - generation; I am pretty sure same for GD - 2012 onward). The immobiliser aspect of the car is controlled by an RFID (or similar) type chip which doesn't use a battery (it takes it's power from the signal used to read the chip) - with an active immobiliser the car will turn over but won't start, however a number of other things could cause the same behaviour.
