In your opinion why did Fyodor Dostoevsky write Crime and Punishment? What was he trying to tell us about life and/or the human condition?
This is a huge question that unfortunately begs for a lot of speculation. We should always be careful enough to realize that we can never really "know" the authorial consciousness of any text.
To give you something to work with, however, I'll posit the following:
-Suffering as the true avenue to God: In 19th century Russian Orthodoxy (Dostoevsky's Church), there was a commonly held belief that God often answered prayers by imparting suffering upon the one praying. This suffering was considered a gift--think of Jesus' command to "take up your cross and follow me"--because it showed that the one suffering was in close relationship to God.
Roskolnikov's relationship with Sonya can be viewed as an example of this. The psychological horror that follows from the murder is terrible indeed, but it is a sort of burden that a sinful man must bear in order to experience the purity of a truly humble partner who has chosen to be on the same level. The love between Roskolnikov and Sonya is a powerful picture of this brokenness as a picture of the Russian Orthodox conception of the relationship between human beings and God.
Maybe Dostoevsky had this in mind when he wrote Crime and Punishment.