the chime unit on the game... it would be a box with what looks like xylophone plates on top of it, under the playfield. underneath or next to that would be a plunger unit which strikes each plate separately, each one based upon certain score values or switches in the game.
the sleeves could be gunked up so the plunger isn't moving with force, the contacts to the unit itself could not be seated right, etc. also check the mounting for the plates themselves. if the plates are sitting directly on the echo box, they will be muffled and not resonate.
watch the video posted above again and listen to the chimes. notice that the slingshots strike the same plate as the bumpers. figuring out which switches activate which chime will help you isolate why specific ones are not tripping. or why the impulse is being lost from the activated switch to the chime.