GE was a big player in the diesel-electric locomotive market, starting with the GE Universal series, then the Dash 7, Dash 8, Dash 9, and Evolution. The division was sold off at some point there, I think before the Evolution. Back in the earliest days the engines themselves were provided by companies such as Cummins but in the 60s GE started building its own prime movers.

As stated by another post, they built the trains but didn't own the track.

However, I'm not sure your conclusion about owning railroads is a nightmare is true. Berkshire Hathaway (Warren Buffet's company) bought Norfolk Southern in 2007 and it's done fairly well since. My understanding is that these are relatively stable businesses because the barrier to entry is large enough to stifle competition.

It was the business that builds trains.