In Hamlet, what is the purpose of Ophelia's remembrance of the former Hamlet in Act III scene 1?
You have highlighted a very poignant soliloquy by Ophelia in Act III scene 1. Remember the context of this scene - Ophelia is being used as bait by her father and Claudius to try and ascertain if Hamlet's supposed "madness" is a result of his love for Ophelia. Remember that Polonius had ordered his daughter to stop encouraging Hamlet, as he feared that Hamlet was just trying to use Ophelia and gain her as a conquest. However, during this scene, with the ever-watchful Polonius and Claudius secretly looking on, Hamlet obviously manages to persuade Ophelia of his maddened state, for after he exits, she bemoans what has happened to him:
O what a noble mind is here o'erthrown!
The courtier's, soldier's, scholar's eye, tongue, sword,
Th'expectancy and rose of the fair State,
The glass of fashion, and the mould of form,
Th'observ'd of all observers, quite, quite down.
To my mind, what this speech does is heighten the sense of tragedy in the play by pointing towards the kind of man that Hamlet could have grown into if his Uncle had not decided to commit regicide, seize the crown and the Queen. From Ophelia's point of view, Hamlet was a "noble mind" and worthy of far more than his present state warrants - thus she ends her speech as follows:
O woe is me,
T'have seen what I have seen: see what I see.
The disintegration of Hamlet's character, as recorded by Ophelia, shows how the tragedy has changed his fate and set him on his path to self-destruction. What could have been will now no longer be.