When you say that the central locking doesn't work - is that the remote control won't initiate the central locking (but it does work if you insert the key) or that there is no central locking at all? If the first, then try a new battery - otherwise, visit an independent auto-electrician. They are likely to be much cheaper than a main-dealer.
It will be broken or shorting cables in the bundles where the cables leave the A pillar to connect with door, I would think.
Pretty common on some cars .. including those. Constant door opening/closing frets the wiring/cables .. and they break. This can affect CL, EW, etc.