frozen peugeot 307 51 plate 2l diesel hdi?

My car got very frozen up in the sub zero temps last night, and wouldnt start due to all the water being frozen!! Was advised by the AA to wait til the water thawed out, and keep the engine warm with a blanket or something. Ive had an old horse rug covering the engine since Saturday, and the water has now thawed. However, she will still not start. The battery is fine, the engine is turning over, but wont actually fire to start. Someone has suggested it may be the immobiliser, but I have no idea. Please can someone give me some advice. Thanks Jo