Though there could be other reasons that Ophelia takes no revenge on Hamlet for killing her father, the one that seems most verifiable is that she has a complete mental breakdown. Although there is some sense in her madness, she seems incapable now of plotting and carrying out an attack on another person. When she is next seen, after Polonius's murder, she is singing songs that reflect both her sadness that her father is dead and her feelings concerning her former relationship and/or breakup with Hamlet. First, she sings,
"He is dead and gone, lady,
He is dead and gone,
At his head a grass-green turf,
At his heels a stone" (4.5.28-31).
This song seems to be about her father who was buried shortly after his death by the king and queen. She will not answer questions she is asked, and she simply tells people to listen as she sings. This is not the way someone who is sane and reasonable would speak to their sovereigns. Some of her other songs address her relationship with Hamlet. For example, she sings,
"Tomorrow is Saint Valentine's day,
All in the morning betime,
And I a maid at your window,
To be your Valentine.
Then up he rose, and donned his clothes,
And dupped the chamber door.
Let in the maid that out a maid
Never departed more" (4.5.47-54).
Here, she sings a song about a girl who will go to her lover's window early on Valentine's Day; the lover will let her in, and though the girl goes in a virgin, she will not come out of the room a virgin. Given the sexual nature of this and other songs, it seems as though she and Hamlet may have been intimate. However, if Ophelia were still in her right mind, she would never reveal such a thing to anyone, let alone Hamlet's family, the king and queen!
When her brother, Laertes, sees her, he says that she is "A document in madness" (4.5.178), and when Gertrude describes Ophelia's drowning, she says that Ophelia was "As one incapable of her own distress" (4.7.177). Ophelia is clearly no longer herself; her mind has deserted her likely as a result of all her unsustainable losses. How could she carry out a revenge plot against anyone?