The back gear is underneath the main spindle, and if it hasn't been used in living memory there will be a certain amount of crud accumulated on it, just 'cos it's the bit underneath.
If the bull wheel chuck and spindle turn freely separate from the pulley (with the half moon key disengaged), and the pulley itself swizzles round freely on the spindle, then the input and output to the back gear are OK, but is the back gear seized on its shaft?
Suggest you disengage the half moon key, and see if you can turn the backgear shaft underneath the spindle without operating the back gear lever to mesh it with the bull wheel..
If so then the back gear isn't seized, so I guess you're looking for a lump of something lodged in the teeth of the gears just jamming up the mechanism.
I suppose the back gear, which is mounted on an eccentric so the knob/lever behind the chuck lifts it into engagement with the driver gear (pulley driven) and the bull wheel attached to the chuck, is actually moving the right distance?
HTH Simon
edit – Nigel beat me to it….edit
Edited By Simon Williams 3 on 12/01/2017 20:10:47