First off â my mistake: itâs Act 4 Scene 5, not scene one. And it opens thusly (lines that merit attention are bolded):
QUEEN GERTRUDE: Â I will not speak with her.
Gentleman: Â She is importunate, indeed distract:
  Her mood will needs be pitied.
QUEEN GERTRUDE: Â What would she have?
Gentleman: Â She speaks much of her father; says she hears
  Thereâs tricks iâ the world; and hems, and beats her heart;
  Spurns enviously at straws; speaks things in doubt,
  That carry but half sense: her speech is nothing,
  Yet the unshaped use of it doth move
  The hearers to collection; they aim at it,
  And botch the words up fit to their own thoughts;
  Which, as her winks, and nods, and gestures
  yield them,
  Indeed would make one think there might be thought,
  Though nothing sure, yet much unhappily.
A bit later, Ophelia comes in, singing. Not of flowers, yet, but alternating between a mourning song, and a very bawdy song that a young noble lady of sixteen years should not be singing in public, just in time for Claudius to hear her.
KING CLAUDIUS: Â Conceit upon her father.
OPHELIA: Â Pray you, letâs have no words of this; but when they
  ask you what it means, say you this: [translation: You want to know what it means? Iâll tell you what it means!]
  Sings
  To-morrow is Saint Valentineâs day,
  All in the morning betime,
  And I a maid at your window,
  To be your Valentine.
  Then up he rose, and donnâd his clothes,
  And duppâd the chamber-door;
  Let in the maid, that out a maid
  Never departed more.
KING CLAUDIUS: Â Pretty Ophelia!
OPHELIA: Â Indeed, la, without an oath, Iâll make an end onât: [Let me finish!]
  Sings
  By Gis and by Saint Charity,
  Alack, and fie for shame!
  Young men will doât, if they come toât;
  By cock, they are to blame.
  Quoth she, before you tumbled me,
  You promised me to wed.
  So would I haâ done, by yonder sun,
  An thou hadst not come to my bed.
[So hereâs a song about a woman having sex out of wedlock because a guy promised to repay her⌠and then he reneges on his promise because she had sex with him]
And then Ophelia exits, spouting seeming madness, and Claudius says to Horatio:
Follow her close; give her good watch,
I pray you.
So Claudius suspects something â whether thatâs a suicide watch, or to make sure she doesnât inspire rebellion â isnât explicitly stated in text. But in any case, Opheliaâs not alone.
Then, Leartes comes in, leading a mob of commoners, who are chanting that he should be king (see the comment of Gentleman, above). And we have this exchange:
Leartes: Where is my father?
Gertrude: But not by him.
That, right there, is a single line of iambic pentameter. Which means that Gertrude literally does not skip a beat to defend Claudius before thinking of protecting her own son.
And now Ophelia comes in and sings her âmad flower song.â This Wordpress article outlines the symbolism of each flower and herb (It also spells out specific actions by Ophelia which are not spelled out in the original). The meaning flies right over our heads, but audiences of the time would have grokked it immediately; Thereâs âGriefâ and âremembrance;â thereâs also âflatteryâ and âdeceived loversâ and an herb commonly used to induce abortionsâŚ
And the next news we hear of Ophelia is that sheâs âDrowned herself.â Who delivers this news? Queen Gertrude â with an overabundance of minute detail of the scene as it happened.
Finally, thereâs the fact that Ophelia was being hastily buried in the churchyard â even though that was strictly forbidden for suicides. The younger gravedigger thinks thatâs because Ophelia was a privileged noblewoman, and getting special treatment. The older gravedigger reminds him (and the audience) that not all people who die by drowning are at faultâŚ
And then I realized that Hamlet had to have the murder plot revealed to him by the ghost of his father, because he was away at school, but Ophelia was there at court, the whole time, and could have seen everything going down. But who pays attention to teenage girls hanging around the edges, or worries about what they see or donât see, amirite?
I do think Ophelia was having a mental breakdown, triggered by grief and shock. But I think it was more of the âloss of situational awarenessâ and âblind to the dangerâ variety, instead of âno longer have the will to liveâ variety.
And thatâs my analysis. And Iâm sticking with it.