What was Hester's conflict with herself in The Scarlet Letter?

I think the easiest way to answer this question is to
consider how you would feel if you were Hester Prynne.  In order to
do this, you must consider the lengthy list of circumstantial conflicts she
experiences:

1. Married to a man she does not love
   and arrives at the New World without him.


2. Falls in love
   with a man she cannot have and has a baby with
   him.


3. Arguably unfairly punished for her "sin" by a
   Puritan society who never relents in reminding her of
   it.


4. So devoted to her faith/religion that believes she
   deserves her punishment, but devoted enough to the father of the baby that she will not
   reveal his secret (and therefore let him bear part of her
   punishment).

Considering these things,
understand the emotional conflict that Hester must have raging inside her.  She feels
truly guilty and is genuinely repentant for what she has done.  This is obvious by the
way she chooses to live, how she chooses to raise her child, and the fact that she wears
the letter until the day she dies.

On the other hand, she
is still madly in love with the father of Pearl.  This is evident by the fact that she
will not, under any circumstance, give up his
identity.

Putting all of this together, consider how
you might feel if the one person you loved most in the world, you
could not have, and you actually agreed with the (in this case, religious) reasons that
prevented you from having him?  This is exactly the internal conflict Hester
experiences.