As Jerry says, we are talking about slop in all the pivot points in the foot start mechanism. If all holes/pins are worn out, there may not be enough throw left to slide the pinion gear all the way into the flywheel teeth or push the button or both. I think I repeated what he said. After hooking it all up, you can operate the foot mechanism from under the hood with a piece of 2 x 4. Disconnect the center tower wire on coil so it won't start. Place in neutral and apply ebrake and stand aside. This will allow you to observe what is happening or not happening. If the bottle cap spacer did nothing, that's good info for you to use to move forward.
I think I see you don't have the negative battery cable attached to the starter bolt. That would be a better place. At any rate, take it off and clean the bolt spot and the cable eye.
What I meant by strap not in play is: if cable was connected to starter bolt.
You don't have a motor won't start case. You have a motor won't turn over case. Two VERY different troubleshooting procedures.
We caught on quick, but try to be precise. We can't see it or hear it or test it from our house.
Other things to be careful of are:
1. The part/battery/cable is "new"
2. I checked that/cleaned that/did that already
3. Sounds and movements and your observations are very important
4. No guessing
You are nice to deal with because you are asking questions and listening and trying....and staying with the post.
