We have a tree in our backyard and we don't know what it is (we are new to the area). It looks like an evergreen, but all of its leaves are now brown and falling off - all of them! Its bark is reddish brown and it is quite tall (two stories high). It is cone-shaped but the leaves are soft and flat, and in bunches on each stem. Very perplexed if it is not an evergreen or if it is showing signs of dying.
It sounds like a Dawn Redewood, Metasequoia glyptostrodies. You'll love it. check out this "article": http://treesandshrubs.about.com/od/commontrees/p/DawnRedwood.htm