I'd recommend you call a certified aborist. Not necessarily to help you take down the tree, though many of them do this sort of work and will probably sell you their services, but to help you identify why the tree died, what kinds of trees might be suitable to replace it with, and how to prevent any replacement trees from meeting the same fate.

It may be that there is some external cause -- such as a leaky sewer pipe -- that could cause other problems with your home and property.

The arborist will appreciate it if you call him BEFORE you cut down the tree. If all he has to go by is your description, all he can do is make a wild guess. If he can see the tree itself, he can make a pretty accurate determination.