Do you think this person will be stuck in poverty forever, given that he's cut off from opportunity by a 2 hour train ride?
Also, I find your claim that people in New Haven or Poughkeepsie (approx 2 hours away) don't know they could find work in NYC simply implausible. I've had random conversations in broken Hindi with auto drivers; when they ask where I'm from and I tell them "New York", they immediately recognize it. Random people in South America, SE Asia, etc all seem to have a pretty good picture of what NYC is. Yet somehow someone from Allentown, PA doesn't?
That implies that it's the American's choices, rather than his circumstances, which cause him to be poor. How is that irrelevant?
They have TV, and the internet. It's not like they are cut off from civilization, with no knowledge of life outside of their immediate surroundings. They know that places like NYC are where the rich people live, and where the jobs are. They just can't do those jobs.
I'm sure we would be better off if all of these people were successful and productive, but it's unrealistic to assume that would happen, for the reasons I've enumerated in my comment. The bottom line is that they have had many advantages, and they have failed in a country that was designed to help white people succeed. Every country has people like this. Look at England.
People tend to assume that if someone is poor, they must be a victim of injustice, and that opportunities need to be created for them. That is sometimes true, but not always. This is one of those cases where it isn't.
What solutions do you propose that could turn these people into successful, productive, happy members of society?
Not often. Regardless, my solutions would start with chipping away at the disdain, indiffernece, and exploitation by privileged Americans. Wealth inequality creates a lot of the problems. Offshoring wealth to Ireland by Apple, FB, etc. to avoid taxes if you want to get even more granular.
Also you are glorifying and over generalizing the opportunities to the Americans you disdain. Just because one has electricity does not mean one has opportunity. I think you'd be surprised to find that many Americans have no realistic way to know where to earn something themselves. 2 Hrs from NYC can be just as cut off from opportunity as 2000 miles.