Is there any way to make the train leave the station?
Solution 1:
Trains will normally start back up automatically after a certain amount of time passes. That amount of time differs depending on the reason the train stopped (reaching a station vs. stopping because an animal is in the way).
However, there is a documented bug where the train stops and never starts back up:
Occasionally, the red/blue train will stop and then not move again until you restart your console. You can still save your game before you reset as this will not make the bug/glitch permanent. Also an escape to the dashboard can resolve this.