Hamlet begins grieving (and mostly, I think, angry with his Mother) but eminently sane; his first talk with Horatio is not the talk of one who has cut ties with the world or is incapable of moving on, and his reaction to the story of the Ghost is almost Sherlockian (he probes for details, looks for contradictions, and so on). Besides, the way in which he pursues the Ghost, and threatens to kill whoever stops him, is not something somebody clinically depressed would act. He's angry and reckless, but he's also direct and to the point (a Doylean aside is that this is the Hamlet of the early pre-Shakespearean versions of the story, but I'm interested in Watsonian analysis here).
However, I'm not sure I understand the scene (narrated by Ophelia) where Hamlet goes to her, holds her hand for a long time, sighs, and then leaves. If it's feigned (and his state right after the talk with the Ghost seemed un-melancholic enough for his Ophelia visit to be feigned), then it's a rather cold and pointless thing to do — simulating a certain unhingedness seems part of his plot, such as it is, but why go out of his way like this with Ophelia? It's not as if he has anything to gain from it.
And if it's not feigned, what caused it? Not her coldness as mandated by her father; Hamlet has other things in his mind right now (and given his feelings at the beginning of the play, I think he hasn't been courting Ophelia for a month at least; aside from the emotional dissonance, had Hamlet courted Ophelia before the wedding his dynastic position and obligations (or lack of both) would have been more present in their talks). The Ghost left Hamlet quite upset with women, but that's not the spirit of his actions as narrated by Ophelia.
Thinking about the scene later on, with "get thee to a nunnery" and all that... Could Ophelia be lying to Polonius to work around his prohibition? Her retort to Laertes when he was leaving for France (basically "I hear you about my chastity, but don't forget to look out for yours, big bro") paints her as not lacking sharpness and energy, and if Hamlet and Ophelia were, before the King's death, in a passionate courtship a la Romeo and Juliet, then something like this would have seemed to her coherent with her feelings and with their relationship (not realizing that after the funeral and the wedding, Hamlet is no longer capable of being in that, or perhaps any, relationship).
Anyway, I'm just jotting down random observations here as I read along (I'm not the first person to do it, and I'm quite certain I won't be the last *g*).