[mike944]

Yes, the CV's can be damaged, even if the boots are still intact, but not the kind of damage you describe. The problem is likely the ring & pinion. At this point, just pick up a used transmission. The broken ring gear pieces have had a chance to get around the transmission internals, and have probably damaged a good portion of the gears. It would be much cheaper to just replace the transmission.

If the problem were your CV joints, with the effects you describe, your CV's would probably be completely separated, maybe a sheared bolt flange.