Answer: Based on your description, sadly it sounds like your pine tree may be dead. If the downspout causes the area where the pine is planted to flood, this could easily have killed it during the winter. Since I have not seen the tree, I would also suggest you consult with your local county extension and/or a professionally trained and certified arborist to see what they think about the tree.
Bare spots in a lawn can be patched. Loosen the soil and work in a bit of compost, sprinkle the grass seed, rake lightly, tamp lightly to assure good seed to soil contact,cover with a bit of loose straw. Alternatively, use a patch kit made for this purpose. After planting the seed, keep the soil damp like a wrung out sponge until the grass germinates.
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