That's good news in the sense that if the sprocket shaft does not have excessive play, then the damage will hopefully be limited. Could you check the final pinion shaft for play, particularly in the direction parallel to the line of contact between the pinion and the sprocket shaft driven gear. For the contact to be insufficient to drive forwards, given that the reverse side of the drive is still intact, tells me that the teeth are still full height (is that correct?), so if the sprocket shaft does not move, then the pinion must for it to be unable to drive the big gear. Could you post some more photos or even better a video showing you levering both gears to/fro, up/down, in/out?