MO, there can be numerous reasons why your birch has not leafed out yet... some more distressing than others.
Did it dry out at all after you planted it? No I keep it watered and it had rain and snow in the Fall and Winter. Did you have any unusual weather events last fall, through the winter or early this spring? This Spring we got more rain than we morally get. We been having a very wet Spring this year, at least a inch or more a week. We are unable to plant the garden for it is that wet.
It would be best if you could post some pictures of it, showing the entire tree, a closeup of a branch and a good shot of the base. I wish I could but I have no camera. There are tiny buds on it, and no the rabbits could not get to the base for I have a tree gard on it. My question is why is there a short coming up at it's base? Isn't this a sign that there is life there? I can bend the limbs of the tree and they will not brake off. It is green under the bark of the tree. If let go will it come out in leaf next year? You see I don't know what would cause this to happen since I planted 3 other trees at the same time last year and they are all in leaf. I let them soak for about 2 hours in water last fall before I planted them. They were bare root trees. Than after I planted them I even soaked the ground after wards and watered them up until it froze last winter.
Sylvia