It's a fig tree but what variety I can't say. Maybe someone from
your area will .

The leaves are definitely a nice 'finger-like'.

It's definitely not a common variety by the leaf shape.  Ronde de Bordeaux's have long fingered leaves like that, but so do a few others.  Strange that it doesn't set fruit.  I would think it should still put SOMETHING on, even in the shade.  Some experts here will come along, i'm sure.

the node has two bump in the pix. leave the tree as it is, and come next spring, pinch off the terminal bud after 5-6 new leaves. that should push the figs if it's able to put on the figs.

I can't manage to obtain a fig tree and they can't manage to get rid of one....oh, the irony! :(

SSaffire, I picked up a branch of the same fig tree that you have shown from the side of the road in Cape May County NJ. The leaves are unmistakable, and before they chopped it up,(new people moving into the house) I was able to notice that the figs were dark purple, to black. Grows like a weed, it is now over two feet tall. The tree was in full sun, I think that it will be a keeper, wish you the best with it, Sergio.

Ok Sergio, just rub it in why don't ya! lol

Sophie, I have a Hardy Chicago shoot in a gallon pot you can have, it all depends how close you are to
South Jersey.

I found this picture on ebay the leaves in the photo look similar to the leaves on your tree


 
http://www.ebay.com/itm/BS-PHOTO-bfh-454-Fig-Trees-/350854806216?pt=Art_Photo_Images&hash=item51b0937ac8

The leaves are more similar to this http://www.ebay.com/itm/Fig-tree-Ronde-De-Bordeoux-/290959210844?pt=LH_DefaultDomain_0&hash=item43be85395c

If you can prove that it is really an RdB;
it so happens that it is one fig variety that is in very high demand right now...

ssaffire27...welcome to the forum...while you are in the process of trying to identify the tree, it might be a good idea to take some cuttings before Dad succeeds in "getting rid" of the tree...this way in case you do find it to be a "keeper" you will have enough material to root some cuttings of your own...hope it turns out to be a real good one...good luck. 

This tree was probably grown from a seed and is not fertile. If you have not seen any figs or embryos (little round bumps above the leaves) then I would look at it as just a wild non-edible fig. In Los Angeles you can see them everywhere, they also grow like weeds and it is almost impossible to get rid of them.
Your dad might be right ... 

Well then the best way to be rid of it is to spray it thoroughly with round up  :)

You can cut the tree to ground level, drill several 0.5" holes at the stump, cover with compost or mulch. This should rot and kill the remaining stump.