Do you have a multimeter? It is pretty hard to tell sometimes without a few readings of voltage at start, idle and rev.

What are your symptoms that made you decide the battery just wasn't charging?

The cracked "object" on the back of your alternator is a condensor for noise suppression. I doubt it would cause the failure unless it shorted out, noisy radio maybe, especially AM.

I had to change alternators twice the last time mine failed. Sad fact is that rebuilts sometimes can be marginal. If your battery is severely discharged, it would be a good idea to charge it for several hours before starting it and charging solely off the alternator. It puts a lot of stress on the diodes which may be marginal on a rebuilt unit.

__________________
Sam

84 300SD 350K+ miles ( Blue Belle )