Answer: Based on your description I am not certain what happened. Overwintering container grown fruit trees can be difficult, as you have discovered. It is possible that the tree was overwatered -- the soil should be barely moist, not sopping wet, because the roots need oxygen as well as water.
It is possible that an insect or rodent damaged the root system during storage (I would suspect mice or voles). It is possible that the tree had become rootbound and strangled itself, with the stress ultimately being too much for it so it simply failed to leaf out. It is possible it was too much of a shock for it coming out of the shed -- the plant can be set outdoors during the day and brought in on very cold nights to acclimate it to the sunshine again, it is possible that the tree survived the winter only to die in the spring -- if the soil dried out and or it was placed in a very windy location, for example.
Going back to the storage conditions, the idea is to keep the tree cool enough to allow a sufficient chilling period but also to keep the soil temperature above freezing. A garage that is attached to the house but not heated is usually about the right temperature, but a detached shed may just be too cold despite the insulation materials.
You might try insulating the pot by double potting it and then heaping mulch or soil over and around it and under it as well to stop cold rising from the floor, or wrapping it in carpet or burlap as you did but also stuffing that with dry leaves and straw or similar materials to serve as insulation layers. I wish I could be more helpful but like so many aspects of gardening it may just be a matter of experimentation until you find what works in your situation.
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