What dramatic purpose is served by the madness of Ophelia?Please help out. This question is from the play Hamlet by William Shakespeare. I'll...

In Shakespeare's Hamlet, when
Polonius is killed by Hamlet, Ophelia joins the other three "children" who suffer or
have suffered the death of a parent.  She joins Hamlet, Fortinbras, and Laertes in
suffering the death of a parent.

Fortinbras begins an
attack on Denmark, only to have his plans thwarted by King Claudius and his own uncle,
the current king of Norway. 

Laertes unthinkingly forces
his way into Elsinore and means to kill the king, who really had nothing to do with
Polonius's death, then allows himself to be manipulated by Claudius into committing
treachery.

Hamlet plays god and tries to determine
Claudius's eternal damnation by not killing Claudius when he thinks Claudius is
confessing his sins and will therefore be forgiven of them and go straight to heaven. 
Hamlet's revenge results in a blood bath.

Ophelia goes mad
and commits passive suicide by letting herself be drowned.  Dramatically, she is one of
four characters who suffer the loss of a parent, and she presents still another possible
reaction to that specific type of suffering.

Incidentally,
she is also dealing with being manipulated by her father, and mistreated by Hamlet,
although it's important to realize that she begins the disintegration of her
relationship with Hamlet by following her father's orders to deny Hamlet access to her,
by returning his love letters under false pretenses, and by spying on Hamlet.  Hamlet
doesn't at first reject her because he associates her with his mother and all
women--that comes later.  He rejects her because, as always, he sees her actions for
what they are--a plot to figure him out, to manipulate him, to "play" him. 
 

Finally, I'll also throw out an additional thought. 
While Ophelia may, indeed, be pure and innocent, the possibility exists that she may not
be so virginal as sometimes supposed.  When she enters the stage, already having lost
her reason, and sings her now famous song, she sings of a dead man and a deflowered
maid.  The dead man, of course, connects to her father, Polonius.  But who is the
deflowered maid?  Also, when Ophelia offers up her imaginary herbs or flowers, some
commentators suggest that one or two of the offerings are natural medicines used in
Elizabethan England to induce abortion.  In other words, one should at least consider
that previous to the opening of the play, Hamlet and Ophelia had a sexual
relationship.