OK so if I'm understanding correctly you're saying that your remote control key does not work.
If you use the key in the door the central locking does work, but you can only do this in the passenger door as the driver door is broken.
If I'm correct then I understand what is going on.
It is quite a common fault that the car will "forget" it's remote controls and therefore the remotes stop working.
In the UK cars were only supplied with one remote so if the car forgets that remote, you've got none which work.
You have to re-learn or teach the car about the remote control again. To do this is really simple, but you need some particular equipment to do so.
You have to have the car's security code. You may have been supplied this with the car from new. In the UK they are not allowed to give you the code with the car. We have to go and buy the security code from the Fiat Dealer - you may have to do the same.
You also need the full version of
MultiECUScan and an ELM cable modified to work with
MultiECUScan. The cables are easily available off eBay.
The software then has a function to let you teach the car about the remote control again.
The other option is that you will have to ask the dealer to teach the car about the remote control again - they can do this for you.