As Peter said, it is quite possibly the inhibitor switch or, seeing as you have had a battery replaced, I'd try a BSI reset first. Failure to carry out this simple procedure after the battery has been disconnected can cause all manner of strange electrical problems.
Although Technically separate, some of the body, chassis and engine control units "talk" to each other and if an incorrect signal is sent or mis-interpreted between them, it could cause this type of fault.
Edited by The-Mechanic on 22/01/2014 at 23:05
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