The basics first: Have you tried moving the wire and the connector around while recording? Try moving the wire around at the mic end. Try (not too hard!) tapping the mic on a hard surface. Does the internal mic work?
What firmware version is installed (use the "tools" part of the menus and scroll down to the last item in the list)?
Can you re-install that version or an earlier version (V1.15 if possible)? Does anything change if you do that? (Installing, for example, V1.20 again will completely reset the camera - a good thing)