Connect the microphone to an output device and gently tilt it from side to side. This is to check for loose connections that may be moving around inside the unit. There should either be a constant signal, or none at all. It will also help you to eliminate the connector as the source of the problem, any hum or earthing sound would likely be caused by a loose connector pin.
Unscrew the capsule from the head of the microphone and try replacing it with an alternative. If the alternate capsule works correctly, then you have determined the original one to be at fault, the rest of the microphone is OK. If the fault remains, try replacing the cable.
Use the screwdriver to remove the locking screw on the side of the case, next to the audio connector. With the screw removed, carefully slide out the inner assembly, taking care not to catch any of the internal electronics on the sides of the case.
Examine the internals through the sealed glass case. Look for any burned out or disconnected components that may be rattling around inside the case. If you can see any damaged components, then send the microphone to a repair technician, as this case is sealed to keep out dust, and to maintain the vacuum state needed to operate the tube.