To answer the original question I have learned through experience that with any kind of machine, or piece there of, there is no such thing as can not be repaired.
I have seen a damaged tooth on a differential ring gear welded and machined back to spec. I have also seen a whole new differential pinion gear made from a hunk of steel. The ring gear broken tooth repair wasn't really a big deal technically so while financially feasible it was still probably much more expensive to do than buying a new one, certainly more expensive than buying a used one. The manufacturing of the new pinion gear would have been horrendously and prohibitively expensive and would never have been done had there been a bill to pay at the end of it. In both cases these jobs were done over many months as time allowed as the proverbial G job, so no financial cost to the requestor.
With any repair if there is no possibility of getting a replacement part then there are only two real real questions to be asked;
- How much is having that part repaired worth to you?
- How much are you willing to pay to have it repaired?
Despite sounding like the same question they are not. The first involves factors unrelated to money like sentiment, emotion, the joy derived from use, etc..
The second is the cold hard reality of finances.
Often the first is infinite, and the second is very finite.
