Mine has been doing the same recently.
Try holding down the button on the end of the right hand stalk and then turn the key to position 2.
This is meant to reset the immobiliser.
The speedo display on mine shows every digit and bleeps when this is done.
I have tried starting it a few times this evening and it has been fine.
Fingers crossed for the morning.
On a possibly related point,my bonnet switch for the alarm is playing up,think its got damp in it as the alarm went crazy on Saturday and would not let me lock the car at all.
Sprayed lube into the switch and it seems fine now.
I don't know if the two problems are related but the alarm problem was evident before the immobiliser one.