Thanks for the photos! At first glance I don't know that that flower/fruit is, but I can look it up. I'm running errands today so will follow up on that this evening.
Here is the tree, and the thing about the base of it is that it has a lot of stuff growing up around it. If you take a rake or a hoe and carefully pull back the grass and dirt, you need to expose the flare. The base of your tree is literally being smothered by the grass and dirt piled up on it.
OldTree-1.png [ 569.36 KiB | Viewed 264 times ]
For reference, take a look at the [url=http://www.dirtdoctor.com/Pecan-Tree-Champion-Weatherford_vq2196.htmstory about a champion sized pecan tree in Texas[/url]. At the bottom you'll see a [url=http://www.dirtdoctor.com/organic/garden/category/id/37/]link to a page with photo links[/url] If you look through those you'll see that the tree needs the flare exposed. You need to be careful not to damage the real roots, but as you get started you'll mostly be in dirt and clearing it.
It should look like this:
or like this:
That will give you something to start with, until I look up the tree or someone else comes along and recognizes it.