No U Don't Have Train.

Why wouldn't they work outside? It's not like they're magically gonna come off the rails once they leave the dome.
All of your trains are outfitted with fail-safe emergency brakes. On power loss, you have about 15 seconds before they are applied and the train comes to an abrupt, unscheduled halt. You can't even tow these things without power.
I thought you said the tracks were in decent shape? Why would the contacts? sliders? come off the power rail for that long?
A) I didn't, I said they are in surprisingly decent shape after being exposed to the elements for a century without any maintenance. B) That power rail isn't gonna be of any use because it doesn't deliver any power.
What do you mean? Why not?
Where does the rail get its power from?
The power grid.
Not quite, but close enough. What do we not have outside?
Of course there is a power grid outside. It's what powered the old world just as ours powers the city.
There used to be one, that much is correct, but it hasn't been used or maintained in a century. Even if you did somehow manage to get part of it working, I still wouldn't trust it. And where would you wanna get the electricity to run it from?
From a substation. We fix up one of those and use it to power the grid.
Great, now you have a local grid attached to the high voltage grid. And what do you wanna power that with?
What? The substations make the power. It's where all the power in the city comes from: Two substations – one in the wall next to this airlock and the other one is by the other airlock.
There is a third one deep below Central Square. These are indeed where the electricity in the city comes from but they don't make it. They get it from a power plant outside, a bit northeast of here.
The dome powered by the outside world? People be believing strange things these days...
I don't have to believe. I was there when the city was built and, more recently, I helped replace a failing generator at said power plant. You might have noticed the power outage.
Uhuh, sure buddy. Since you've been doing nothing but spewing nonsense all this time, I'm just gonna have one of our guys drive a train up there and we'll see what happens.
I'll get some popcorn; watching this is gonna be fun. Wouldn't be the first time a train got stuck in these tunnels...