Paul was a rather depressed person for a large portion of the story and it is safe to say that Paul had several suicidal tendencies. Paul was very often depressed throughout the story. He was extremely introverted, dissatisfied with his life and felt isolated almost all of the time, as if no one could understand the way he felt and how he wanted to live.
According to The real world suicide FAQ these are quite often syptoms of people crying out for attention to their problems by attempting suicide.
"People can usually deal with isolated stressful or traumatic events and experiences rather well, but when there is an accumulation of such events over an extended period, our normal coping strategies can be pushed to the limit." The real world suicide FAQ
Paul had led a very rough life. He grew up in a Calvinist household which does not allow the luxuries in life that Paul so desperately wanted, and felt he deserved. Also, there are some suggestions that Paul's father was physically abusive to him, and it is almost certain that he was emotionally abusive to Paul. In addition to that, Paul and his father were at the most Low Middle Class, if not below the poverty level. All of these things can make a high school boy very insecure about himself and his life. It can make him doubt his self-worth and possibly consider suicide as an alternative.
However, I think Paul never attempted suicide because his defense mechanisms kept the terrors of his life in check. These mechanisms included his vivid imagination, a strong sense of humour, and the music of Carnegie Hall.
These were effective in keeping Paul's life bearable. But when Paul saw all that he could have in New York, he let his defenses down. I think when he saw "the dark thing in the corner" it might have been suicidal thoughts he was talking about. When he was in New York, he thought he had defeated them once and for all so he let his defenses down.
That would have been fine had Paul not run out of money. Once he saw he was in danger of being caught and his "good life" being ended, the dark thing came back and Paul was unprepared.
When the train came, it presented a window of opportunity for Paul.
The dark thing had his chance to enter Paul's mind and take over. It
wasn't until it was far too late that Paul realized how wrong he was for
jumping in front of the train. He realized when the time was about to run
out that he will never see all the things that he wanted to see. He will
never get to do all the things he wanted to do. The end came swiftly and
without mercy.