What battery did you put in? A normal 1.2 petrol battery isn't really up to the job. Because the power is produced chemically you'll find when you stop driving the voltage in the battery is high (13+ volts) and can deliver more power but leave it a few hours and that will drop down to a more normal level 12ish volts, also when warm the engine will turn over nicely when the car is cold the 1.3 multijet is much much harder to turn over resulting in lower cranking speeds.
Throw in a dirty corroded engine earth and you'll struggle to get it started of the motor, but pushing will give you higher cranking speed so much easier to start.
What are the specs of the battery you have fitted ?
You could also try my battery maintenance video
Which shows the standard battery for your car 50Ah and 350Acc compare that to what you've had fitted