Check the metal nib on the key is clean, and likewise, the ring on the ignition barrel: give both a thorough clean and dry down. It is crucial that the key is able to carry out an unimpeded 'handshake' with the immobiliser through the interface of key nib and ring; without such, there will no start. This is, of course, the lowest level of intervention. If the car still does not start, it could be the immobiliser at fault or the ECU. Either/both ways you would need to interrogate the code on the dash and have service proceed from that point. If the battery is good, and the battery in the remote key is also good, there are few options other than to go through a short process of elimination before handing it over.