@Faun147,
In asking "what constitutes the self," I think a good place to begin is sentience. If sentience is not the foundation of what constitutes the self, it is certainly a ubiquitous characteristic- which means it probably has some kind of importance.
To use some of Freud's ideas here, the results of sentience take form early on- with the recognition of pain, desire, etc. This creates awareness of causality, etc. Biological make-up and material conditions lead to level of intelligence, aesthetic tastes, morality, social skills, creativity, and so on. These also decide what god you worship, what food you eat, and who your friends are. In this manner, biological makeup (and/or a soul if I'm missing something here :-) ) and material conditions are the components that fit into sentience like pieces of a puzzle. Without all components, we have no picture- no self. Sentience alone is nothing more than sentience-- without anything to perceive, sentience is but a singular point, with no selfhood. There are many people who desire to rid themselves of the self and attain this point of singularity... but maybe this point is not an end, but a beginning.
In regard to awareness, problems of the self come to play. There are parts of the mind of which we are unaware. This means that we are not aware of all things we perceive. It is my opinion that awareness increases as we grow older, and wiser; and that awareness is the most important aspect of wisdom. Then, of course, in matters of wisdom at this fundamental level, sensitivity plays a large role as well- otherwise we will not be aware of things because we fail to perceive them in the first place.