I've tracked the film down!

There is a watchable and downloadable copy at The Internet Archive - Steamboat Bill Jr..
Guest Nahrum is gives us the position for the prison scene - about 45 minutes into the film. The words of the Prisoner's Song are on the wall and you can actually see Keaton singing lines from the song.

Are there any other songs where you could claim "I learned it from a silent movie"?

Quack!
Geoff the Duck.