There is a common problem with the wiring providing voltage to the receiver for the key fob. The symptoms will be the key not working at all. This cannot be fixed with a new key fob battery. This usually occurs in LR3s that have had water ingress due to faulty sunroof drains. Water pools in the door sill and corrodes the wiring splice.

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TO FIX:

You must pull the door sill on passenger's side and locate the splice in the wiring bundle. The wire junction you are looking for is white with green stripe.It is typically two wires to one. (e.g. three wires total). The fix is to re-splice all of the wires