Ok, I'm in. First, you must remember not to assume anything. The schematic shows the PTO switch in the disengaged position. When you raise the deck to the up position you engage this switch, where it needs to be to start the engine. By disengaged they mean in the normal operating position, NOT for starting. That said, here goes.
As I read your posts my first question is, is the key switch the correct one. The first thing I would like you to do is take the key switch and verify each terminal is in the correct position as the schematic. If you look at the switch you have out of the engine, this is what you should see on either the terminals or on the back of the switch.
Terminal #1 should be labeled L or A for lights or accessories
Terminal #2 should be labeled B for battery
Terminal #3 should be labeled L or A for lights or accessories
Terminal #4 should be labeled M for magneto
Terminal #5 should be labeled S for starter
Terminal #6 should be labeled G for ground
Please check each of these carefully, as this will tell us our next step. I spent 34 years teaching this stuff to people ranging from 11 - 60 years old. My methods are crazy and at times people didn't like to do it my way, but when I'm done it will be running. Remember slow and patience. Post back what you find and we will go to the next step.