One place where I worked we built PA systems and echo units for clubs etc... my job was repairing radio & TV's and sometimes I used to help out building and repairing PA systems.... lol ya' can always tell when it's a woman artist.... mic grille covered in lipstick, a Tom Jones artist grill all bashed in when he dropped the mic, sometimes there were half a pint of ale inside! We supplied Beyer mics, we did Shures once in a while but they weren't as popular.
One thing you don't do with mics is put them on top of a radiator I've seen done, could be the capsule.... doesn't help at all, could this have happened? The only thing is to get at the transformer and capsule end to check with Ohmmeter.
The wire might not look broke.... but the conductor inside might be. Just like speakers if they not melted voice coils you can bet it's the wire from the voice coil to the flexible lead, I've seen em broke at the lead end or just were they come from the voice coil.... repaired loads like that.
Dave