Thank you for the great pictures of the problem with you monkey puzzle tree.
Here is information about problems with this tree.
http://www.ipm.ucdavis.edu/PMG/GARDEN/PLANTS/araucaria.html

Based on the pictures of branch die back, drought stress might be the cause.
Did you irrigate the tree in the last several years? Monkey puzzle trees like regular irrigation.  Drought conditions from recent summers are impacting a wide range of trees.  There are not any common disease of the tree per the link above

In terms of management, the growth of new branches indicates that the plant is still alive.  Trim the dead branches and provide regular irrigation from May-September. 

It looks like the planting location is on a slope.  Consider using drip irrigation and making a small berm on the downhill side of the trunk to collect water to soak it into the root zone.

Please let me know if you have further questions.

Weston

Your conclusion about my lack of watering was spot on.  Thank you so much, I love the tree. I will change my evil ways immediately.