Hi,
If the key blade opens the door and will start the car then the key blade and immobiliser chip is ok. Your problem is with either the remote fob ( dead battery or broken circuit board ) or just needs re-adding to the car with op-com or similar as you have the DTi.
Is there a red light on the fob when you press the button? ( some fobs don't have red lights! ).
May be worth putting in a new battery and making sure the battery holder has not broken away from the main board. If that's good then an op-com should fix things for you. You will also need your security code if reprogramming is required.
Has this fob ever worked?