BOG EASY TRAIN STATION -- what I experienced
Short Answer: To the left of the Ticket Booth is a wooden platform and a power box. While Oswald is zapping the power box, have Mickey place a TV Sketch on the wooden platform. After you go through the Projector Screen from Old Town to Blot Alley, you can turn around and come right back. Anyway, it has to be later, when you come back, so the station master will be on the dock. Talk to him. Drop a TV between him and the station, to get him to move closer to the station. Talk to him. Drop another TV closer to the station. If necessary, talk to him again and drop another TV. Soon, he will say that he will open the station, and will be inside. TO COMPLETE THE TASK, you must go and talk with him while he is inside the ticket booth, and get a pin. Later, you must talk to the Conductor at the Mean Street Station.
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I suggest buying an Anvil from Ventureland and coming back out, before going to Bog Easy. Anvils will come in handy to drop on enemies and things.
When you first arrive in Bog Easy, you take care of a Beetleworx machine generator/replicator, by painting and zapping the power box next to it, or thinning the red eye inside the doors, when it puts out a new machine. If the doors are closed, destroy the machine on the dock, so it opens the doors when it puts out a new one. (Anvils are great to drop on them.)
When you enter a store, buy a TV sketch, that you can use to energize the train platform (and distract enemies and even climb on).
IF YOU NEED MONEY, there are three chests on top of the Bog Easy Store, and one chest by thinning out the thing left of the store door. You will set up a routine: chest next to the store; crates next to an area sticking out; paint and jump to roof; face the cliff and go all the way to the right corner to spin three chests; thin an orange trap door in the store's roof and drop down; use your "open door" button; use your "open door" button; and you are outside, to go through the routine again -- and are a hundred dollars richer! It keeps resetting every time you drop into the store, so you can get as much money as you want.
At some point, exit the back door out of the store, and you meet the train station master, way far from the train station. Talk to him.
Go take care of the Beetleworx generator that is on that dock, and spin away the jumping chicken enemies along the entire dock. Leap over thinned sections of the dock (aware that the frogs keep thinning the dock.
To the left of the Train Station Ticket Window is a wooden platform and a power box. Get power to the train station by quickly tapping the button that has Oswald electrify the platform power box that is left of the train station. While Oswald is automatically zapping, have Mickey drop a TV on it. It may take a couple tries to synchronize both activities.
THE STATION MASTER STILL IS NOT EVEN ON THE DOCK! Even after you have made sure there are no more enemies, even down by Louis' shack, and no matter how many times you go back and talk to him, he still will not come over.
Go to Old Town and do other stuff. I believe you must bomb or get the Beetleworx to break the wall between Old Town and the projector screen to Blot Alley AND you must go to Blot Alley in order to get the station master to come to the dock.
After going through the projector screen, you can go back through the screen and do more stuff in Bog Easy, including the Train Station -- or you can come back later (but not too much later or the earthquakes will permanently destroy it.)
At some point, the station master will come to the dock, and tell you he wants to watch TV instead of work. You have to lure him to the station by getting him to move little by little toward the station.
Drop a TV between him and the station, so he will walk a little bit to watch TV. Talk to him. Then, drop another TV closer to the station. Talk to him. It should not take more than three TVs for you to get him to open shop.
When he is inside the train station ticket booth, talk to him again.
At some time, report back to the station master in Mean Street South Ticket Booth, again, too, to get full credit. (He is the one who originally assigned you to fix all the train stations, and most Quests have a "Turn In" person.