The northeast and southern California are both perfect places for rail transport, because there are many cities within fairly close proximity. In the northeast, where passenger rail is already well developed, taking an Acela high-speed train between, say, New York City and Washington, D.C. is faster than flying, since you don't have all the time wasted getting to and from the airport, checking in, going through security, etc., plus it's just more enjoyable, and you can get some work done while you travel with on-board WiFi, have a meal, etc.
The long-distance trains are largely aimed at tourists these days, because it's a great way to see the country without all the stress of driving. Some people love road trips and that's fine, but there are others who like trains because you sleep on-board, walk around, eat in the dining car, and socialize with other passengers. It may not be profitable, but the economic logic is that it boosts tourism for the country as a whole, and in particular in the cities served by the train. Many overseas tourists come particularly to take rail tours.
Additionally, the train provides an important service to people travelling with a lot of gear, for instance for camping, hunting and fishing. Either they don't want to drive, or the place they need to access is not readily accessible by any other mode of transportation than the train. You can arrange to get dropped off in the middle of a forest or desert where there are no roads, for instance.
The trains in the northeast, where they are aimed at regional business travellers, are generally on-time and are even profitable. As for the long-distance trains, they are often late, but the tourists who use them are just happy to be on board and don't generally care if they arrive a couple of hours late after a 2-day train journey. The lateness occurs mainly because tracks are not always repaired in a timely manner, and passenger trains have to pull aside and let the freight trains pass, since it's the freight companies who own the tracks for the most part.

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You ruin the life of the train driver and possibly the driver's family as well. You might also cause severe mental trauma to anyone witnessing the event or having to pick up bits of you afterwards. You ruin the lives of the friends and family closest to you. You might even survive for an entirely natural lifespan unable to do anything for yourself and having to be a massive burden on those who your selfish actions force into caring for you.

Suicide is rarely painless, rarely instant, often horribly painful, and there's rarely any certainty that you'll do it correctly and end up dead. But the ripples of such a selfish action cause immense damage to others.

I got on the wrong train last week and I was asked to pay for a large fine on the spot. I thought my ticket was valid but it wasn't. I showed them the ticket I had.

Since I didn't have the fined money, they took down my address and name.They said they would mail me something that would have instructions on how to pay for an even larger fine and a possible court date.

I feel so stupid and embarrassed at this whole thing. Its been a week and I still haven't heard from anyone by phone or mail.

What should I do?

Ah well, yes it's a bad habit for anyone to cross railway tracks, especially children, because you can get hit by a train. Trains can sometimes be moving very quickly and silently, so you might think there's no train coming, try to cross the track, and then you get hit.