If the machine is working but the escalator is not moving, there has to be a problem, albeit caused originally by dirt jamming the escalator. The escalator is driven by a connection to the main cycle, therefore if the machine is running and escalator is not, then the connection between the machine and escalator is faulty. Either it's slipping past (which will not be doing the machine any good), a part has been removed to allow the machine to work on free play, or a part has broken because pulling the handle while the escalator is jammed has forced the issue (unlikely).
I don't think it's easy to see from the photos we have. Can you track the escalator connection back to the machine cycle and photo all of that area so we can see if anything is missing.