Not entirely sure what you're meaning by 'key slot missing a hole'. If you mean the ratchetey looking thing (the pawl) doesn't seem to be able to be hooked up to the push rod, then for that you need to grow a 3rd hand. Mind you, yours isn't in the car, so it should be easier I guess.
You need to thread the pushrod (with the button & spring on it), down the shaft of the handle. Make sure the bend at the other end of the rod is arched upwards, ' ^ ', mot downwards like this ' v '. When the end of the push rod is nearing the base of the shaft, you need to pivot the pawl so that the head of the pawn (in your first photo, it's the little piece in the center of the handle hanging down) fits up in the arch of the pushrod, so that when it's fitted, it should look something like your second photo.
When in the car and the push button pops out, it's a right pain in the donkey to fix up, but it is certainly possible. Just a very fiddly operation.
