Mr. Davis -
I Reinstalled OSX and no change.
Here's something I noticed and it probably doesn't mean a thing, but. . . .
It gets stuck when it is "Importing mailbox Sent Messages -".
When I just tried it, it got stuck on Impoted 10931 of 13015 messages.
Then I tried again and it got stuck on Imported 10920 of 13004 messages;
Then one more time for the heck of it and it was Imported 10909 of 12993 messages.
So each time I started it was 11 messages less than the time before and each time it got stuck it had 2084 messages left to go!
Not sure of the next steps . . . . sigh
That means that one or more corrupt messages is in a "Sent Messages" mbox folder. Referring to your first screenshot, it looks like you have two such mailboxes. Move them both to the Desktop, then launch Mail again and see whether it succeeds in building the index. If it does, you can try to import one of the mailboxes you moved (File > Import Mailboxes...). The imported messages will be in a new mailbox, and you can then move them wherever you want.
If successful, try importing the other mailbox.
At some point, you'll probably run into an error. Then you face a tedious process of elimination. Make a copy of the mbox folder. From the copy, delete about half of the thousands of emlx files it contains, each representing an individual message. Try the import again. If that succeeds, try to import half of the remaining messages. Continue in this way until you've isolated the corrupt files.