Answer: Based on your description I am not sure if they are dead or alive. Usually bare root plants will leaf out in the spring close to their normal time, but maybe a little late. If they dried out last fall or dried during the winter or this spring, they may be dead. You can check for live wood by looking for green just inside the bark, the buds should be plump and firm, the wood should be somewhat flexible. Dead wood has gray or dull brown coloring, the buds are dry and hard, the branch tips or branches are brittle and dry, they snap easily in your fingers. Dead wood can be removed, if there is live wood left they may be able to grow.
I would have expected these to have shown signs of life by now. Bare root plants are special in that they should be hydrated prior to planting by soaking the roots in water overnight. Then the soil should be kept moist until it freezes -- and you would continue to water the entire next growing season if rain did not keep the soil moist. Birch trees are especially susceptible to drying out, the roots should never be allowed to dry out. Usually our spring weather is wet enough combined with snow melt that the soil stays moist enough on its own without watering... if they are still alive I would recommend keeping the soil moist and hope for the best.
You should mulch them with several inches of organic mulch over the root area (not up against/touching the trunks) to help keep the soil moist, and when you water apply it slowly and thoroughly so it soaks down deep throughout the root area. You can check the soil with your finger to see if and when you need to water. Good luck with your birches.
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