Have the battery checked and it could be the starter motor, on these the battery has to be tip top in order to start the car from cold. The starter has to turn the engine at 750 rpm before the injectors will fire and this requires maximum grunt when cold, I found when my starter went it was fine once it was warm but a shit when it was cold.
Here's a quote from another thread on the same subject.
What you describe regarding starting the car does seem to be something that happens with the starters on TDCI's. One of the main reasons mine went was put down to lack of use as over time the steel shaft that runs through a phosphor bronze bush gets dirty and some of the dirt gets in between the bush and the shaft increasing the friction and putting more and more load on the starter, eventually getting to the point where it really struggles and ultimately fails to crank the engine fast enough. The problem is that without testing the starter or putting a known good battery on the car some people will put the sluggishness of the starter down to a failing battery only to fit a new one and find there is no difference when trying to start the car.