Trying to figure out what kind of tree is this. It doesn't flower or do anything remarkable, but it is also growing in the shade and doesn't look too healthy.

Take a picture of the whole tree. Take a picture (more closely, with your hand in it) of where the leaves are attached to the stem.

Near as I can tell from these images, the plant looks like it has opposite arrangement of simple leaves, with some big fat terminal buds. The bark on the younger trunk and branches reminds of cherry bark. This leads me to believe that this could be a Syringa reticulata - Japanese Tree Lilac.

Might be odd to consider, but it could have been planted before you got there. You haven't given us information on history of this site.

Thank you John. Here are some more photos. The tree has been here for a long time. I have no idea how long. It doesn't flower so don't think it's a lilac , but it does have leaves similar to a lilac. Hard to get good photos because it does t have stems low down. It's stuck in a sliver of dark space towards my neighbors. I would remove it if it wasn't for the fact that the few leaves it does produce creates a privacy screen. Trying to figure out how to make it grow even more leaves, so it would be helpful if I knew what kind of tree it is.

I thought at first those were borer holes in the last picture but they look too shallow and then I noticed a couple of fresh "gouges" to the right of the old wound. Are woodpeckers going at the tree? If it has some kind of insect/disease problem you might not be able to get more leaves on it.

sooby said: I thought at first those were borer holes in the last picture but they look too shallow and then I noticed a couple of fresh "gouges" to the right of the old wound. Are woodpeckers going at the tree? If it has some kind of insect/disease problem you might not be able to get more leaves on it.

Those are bird marks. Not insects. Sapsuckers