What (psychological) afflictions are related to or bare the symptoms
of having one eye that is "alive" and the other being "dead" or
unemotional.

When you look into a person's eye, and you notice that the right eye
is alive and full of emotion, while the left eye looks dead and void
of emotion, what problems could that hint to?

I doubt that this is a psychological problem. It's more likely to be
neurological, or a vision-related condition.

Another rather obvious thing that can cause this appearance: a glass
eye. Ever notice that Peter Falk, as Columbo, has an odd stare? That's
because only one of his eyes is a real eye. The other is prosthetic.

The psychological disorders that could account for this condition are:

Body Dismorphic Disorder. 

This is a condition whereby the person feels that certain parts of
their body are ugly, or degrade their body in some way. It is possible
a person could feel this dissociation with their eye and therefore
apply these feelings of lack of emotion.

http://en.wikipedia.org/wiki/Body_dismorphic_disorder

Schizophrenia

A much misunderstood condition that DOES NOT imply split
personalities, rather an impared perception of reality. i.e.
hallucinations; inferring erroneous conclusions from randon stimuli.
e.g. I saw my friends christmas lights flashing in time with my wife's
car indicator so they are having an affair.
These perception disorders could lead to the view that one eye is
"alive" and one "dead".

http://en.wikipedia.org/wiki/Scizophrenia

Manic Depression (Bipolar Disorder)/ Scizoaffective Disorder

Both can similarly lead to disoders of perception in certain phases of
the disease in the same way a scizophrenia

http://en.wikipedia.org/wiki/Manic_depression
http://en.wikipedia.org/wiki/Schizoaffective_disorder

Please note that these conditions affect the perceptions of the
observer. Therefore there are a number of possibilities for yourself:

1. You know a person in whom these symptoms are present.

There are 3 possibilities:
a) There is no real problem with them. You a perfectly normal. You
have simply seen something about their eyes that is not real.
b)MOST LIKLEY They have a physical condition such as a glass eye,
cranial nerve palsy, squint, partial stroke that has led to your
observations.
c) You as the observer have a condition that has led to a delusion of
your perception making you think that the person has one dead eye and
one which is alive.

2. You are the person who you feel has such symptoms present.

a) There is no real problem with you, you have simply seen something
about your eyes that is not real.
b) You have one of the psychological conditions mentioned above.

I think it is schizophrenia.