And you may be thankful if it is dead. Our town will NOT let them be planted within the city limits. The wood has very little strength and everything from twigs to large branches come down at every opportunity. They are a constant chore to rake around. The roots get into anything and everything and will crowd out other plantings.
We had one when we bought our current house and that was OK because all of our neighbors wanted to cut it down. They did, so I just did some of the clean-up work. It took 3 summers before I could get the wood aged enough to even think about burning it because it is so full of water.
As for your willow that's not growing or looking alive, if it was mine, a liberal application of a flame thrower would be in order. However, willows are among the last to leaf out in the spring. You can tell if the larger branches are alive by gently removing the outer layer of bark with your thumbnail and seeing if there is any green color showing. The green is a sure indication of life. As for your losing its branches, that's just normal for willow trees. If yours really does die, you will have mushrooms in your yard for years following the path of the major roots.