It looks like there is green corrosion (the dreaded "green crusties") where the insulation is broken, if I'm seeing that right (just before it goes into the back of the connector). But the pic is a little blurry where the white wire goes into the connector itself and it looks somewhat green there, too. That could very well be the problem.
You might want to strip back the insulation on the wire, back to where the wire is not green, then you could measure the voltage there to confirm that the problem is between the corroded part and the connector. They probably make a pigtail to replace the connector and a short bit of the wire.
You might want to strip back the insulation on the wire, back to where the wire is not green, then you could measure the voltage there to confirm that the problem is between the corroded part and the connector. They probably make a pigtail to replace the connector and a short bit of the wire.