In the Star Trek reboot (2009), since Nero and his crew travelled back in time, why didn't they just take off and warn their homeworld of its imminent destruction? The ship had warp drive, did it not?
Nero was captured by the Klingons and tortured for almost 25 years. My guess is it drove him insane, leaving nothing but revenge in his mind.
A practical answer of possible universes:
If he could successfully warn his homeworld and prevent its destruction, then that would create a causality paradox where the new Nero would not have a reason (or ability) to go back in time to warn his homeworld. Therefore, reality wouldn't allow such an action to be possible (assuming reality only exists in a state where it has referential integrity or it would not exist). This sucks because: The average person has no understanding or interest in paradoxes when it comes to entertainment... so who gives a crap.
If he could successfully warn his homeworld and prevent its destruction, then he would diverge into a different alternate reality where there are now two version of Nero... and the old reality has non (and no homeworld). Alternate reality theories are selfish because the reality only shifts for the active traveler and nothing changes for anyone else. This sucks because: Changing anything doesn't effect Kirk or anyone else not on Nero's ship... so who gives a crap.
Ultimately, what it comes down to, it's just a narrative loose end that the writers either weren't intelligent enough to identify, were told to ignore it as irrelevant to the narrative, or they just didn't cared. Star Trek writers are notorious for not caring about things that don't make sense within a plot... this is no exception.
I know there are plently of good answers here already. But this was sniped from the script itself:
Captain Nero(N) to Captain Pike(P).
P: You're blaming the Federation for something that hasn't happened...
N: It has happened! I watched it happen!
N: I saw it happen!
N: Don't tell me it didn't happen!
N: And when I lost her, I promised myself retribution.
N: And for 25 years I planned my revenge against the Federation.
N: And forgot what it was like to live a normal life.
N: I did not forget the pain.
N: It's a pain that every surviving Vulcan now shares.
N: My purpose, Christopher, is to not simply avoid the destruction of the home that I love...
N: But to create a Romulus that exists, free of the Federation.
N: You see only then will she be truly saved.
So you can see his intention wasn't only revenge, he wanted to destroy the Federation, get revenge on Spock/Vulcan, save Romulus and make Romulans the dominating race in the alpha quadrant.
Maybe he tried and nobody believed or he didn't try because nobody would have believed him anyway.
Of course, he has very advanced technology to prove he's from the future, but in a tyrannical government that tightly control the information he's likely to be seized and jailed forever or killed while the government keeps the technology to advance the empire.
Another issue with warning his home-world is that he might have driven himself and his wife out of existence. He wanted revenge on Spock, not to save his people, specially when it might not only not save his wife, but totally erase her.
Nero was driven mad with rage after witnessing the destruction of his homeworld, and knowing it also spelled the death of his wife, and his unborn child. He was supposed to be their savior – he had promised her, and she had believed him – and now he was watching them all burn.
Unable to cope with his own failure, he lashed out against anybody that he found remotely culpable. He killed the Romulan senate, whose inaction had hindered him start, and then against the Federation that had failed him. He had put his faith in Spock, come to rely on him to save Romulus, and so he resented him the most.
When he arrived in the past, Ayel saw an opportunity to return home. But Nero saw something different; he saw his destiny to return to Romulus a hero; to wipe out the Federation that would one day betray them, and to claim the red matter "weapon" for his people, that they may rule the galaxy.
Now imagine that thought, festering in his mind for 25 years in a Klingon prison.
Imminent destruction? In 2258 the Hobus supernova was still 129 years in the future.
It wasn't at the top of his to-do list.
But the film did indicate that he planned to save his homeworld in the alternate timeline. As Nero said in the film:
My purpose, Christopher, is to not simply avoid the destruction of the home that I love...
He DID go back and warn his homeworld and in fact, he saved it from destruction and lived happily ever after.
However, as established in the TNG episode Parallels (And backed up by the plot of the movie this question is about), the Star Trek universe has an unlimited number of different realities that have an unlimited number of alternate possibilities existing simultaneously.
This movie follows one of the more action packed alternate realities.