What can I do to save my Japanese maple tree?
I have a Japanese split maple about 8 years old and 5 feet high. The trunk is about 4 inches in diameter. The tree was absolutely full and beautiful in the spring and summer of 2013. At the start of winter, it did not lose all its leaves, and some branches appeared dead at the start of spring 2014. During the summer of 2014, it only had a few branches with new leaves. Again the old leaves never fell. I live in Pasadena, Maryland, and all the trees in my neighborhood have green spots, and there are some now on my maple's trunk. There are no other signs of pests or disease. The bark is splitting on the main trunk.
Do I trim all the branches back with the dead leaves at the beginning of spring and see what happens?
It takes energy for a tree to sever the connection with a leaf so that the leaf can fall off in autumn. When leaves remain on a tree is can indicate that the tree is not doing well. Your description of a tree with hanging dead leaves, not leafing out, and bark fall off all indicates that your tree is dying.
The green spots on the trunk have no impact on the health of the tree. The greenish-gray spots are lichen (part algae/part fungus) which live on trees, but only use them for support. They don't take any nutrients or energy from the tree.
If some of the root system of your tree is still alive, and some branches are still alive, then this spring you can try rejuvenating the tree. Prune off all dead branches. Dead branches are brittle and snap easily. They do not have plump swelling live leaf buds, and if you scratch the bark, you will not find any green underneath.
If all branches are dead, your tree is dead.
If most of the branches are alive, and the shape of the part left alive is acceptable, as you said, you can see what happens. You may get some new growth if the tree is not too far gone. Be sure to water during droughts for the next two years to help it come back.