The fruit is a drupe, so you can rule out Malus spp. Likely a cherry or other Prunus sp.

If you don't get a definite answer here, you might ask in the Fruit & Orchards forum. Can you take a larger, clearer picture of the pit?

They can also advise about pruning off the dead branches and evaluating what's left of the tree.
http://forums2.gardenweb.com/forums/fruit/

Was the fruit soft when you tasted it? If not, it probably wasn't ripe yet. There are some plums which are green when ripe, but it's not a common color for ripe fruit.

My first guess just looking at the picture was a crabapple. I grew up with them all over the yard. They are a super tart fruit with a hard pit and that is exactly what they look like!

My first guess ... was a crabapple ... a super tart fruit with a hard pit

Crabapples, like apples, have several individual seeds and not a single large pit. See the last illustration on this page:
http://www.nhm.ac.uk/nature-online/british-natural-history/tree-survey/identify-cherries/cherry-lookalikes/crabapple/index.html

The fruit definitely tasted unripe, so that could be the reason for the sourness. I will try to get a larger pic of the pit and leaves and upload on an external website. Thank you all.

What makes you think it is a drupe?

All indications are that the fruit has a single seed surrounded by a stony endocarp, which would make it a drupe.