Hi Plum Tuckered Out,
I just love your name! Unfortunately there isn't enough info here for us to be very helpful. Did the nursery plant this tree or did you? If they planted it there should be a warranty, usually about a year. I don't know what the warranty would be if you are the one to plant it.
Without knowing how you planted your trees, how often and deeply you watered, how deeply the tree is planted, if you fertilized (a 'no, no' for newly planted trees and shrubs) and if and how you mulched it would be difficult to say what is going on.
Maybe the top is grafted, the graft failed and the top died and now the rootstock is sprouting. Do you see any line on the trunk of the tree above where the leaves are growing that could indicate a graft?
...there are new leaves on the trunk of the tree no leaves have come out on the branches.
No, branches are pruned to remove dead wood, to insure the direction of growth or to thin the tree.
...do I need to prune the branches for the leaves to grow and if so how much?
Are the dead branches on one side of the tree only or spread throughout the canopy? On one side could suggest verticillium wilt or some type of trauma, possibly root damage to that side of the tree.
Also, my 2 yr old Asian pear has leaves on perhaps half of its branches do the bare ones need to be pruned?
How about some pictures of your trees?
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.