Elsewhere In My Yard

We've talked on two occasions about the potential removal of my gigantic rock. Despite all the great suggestions, I still haven't decided what to do. We'll discuss the rock again another time. Today, let's move into the front yard, and talk about trees.
This tree straddled the property line between my neighbor and the town. (Our lots are separated by a path to an elementary school.) We all knew it was dying "“ leaves had stopped appearing, and huge branches were falling on a fairly regular basis. Finally, last week, the town sent a tree-removal crew.
When it comes to chopping down trees, I'm a novice. I should probably do some intense tree research, but I'm home sick with a 103º fever. (Well, it was 103º about twelve hours ago, and has been falling ever since. But still. Too tired for dendrology.) Any tree experts out there care to provide a diagnosis? Think our other trees are secretly hollow? How can you tell how old a tree was when the tree doesn't have rings?
One more pic, to give better perspective, after the jump.
Note: If this post doesn't make sense, just nod politely and go about your day. I may be delirious.