Answer: It's a little late in the season to be pruning to promote new growth, so I'd wait until next spring to do some remedial pruning. The branches are still alive if, when you scrape the bark away, you can find green tissue. If the tissue is brown, that part of the branch is dead. I don't know why the branches didn't produce new leaves. The tree could be stressed for some reason, or leaves formed in the spring but then fell off do to insect or disease damage. I'd leave the tree alone this summer but prune it back slightly in the spring to encourage healthy new growth. If no new growth appears by next summer the branches are probably dead and should be removed. Good luck with your tree!
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