have a scag kawasaki, won't start by key

I can jump start with a hot wire from battery to spade on solenoid, engine will run just fine. I believe that eliminates all safety switches, i.e. neutral left and right, brake and seat as problems. replaced the relay. Have 12 v from the green wire of switch to relay, start position. have 12v from switch, red/yellow to relay. get no voltage on the green/white wire to the solenoid from the relay. This is what lead me to believe the relay was bad. this is how I believe the relay works, Power comes from the start switch when placed in the start position, via green wire to terminal 85 on back of relay and its ground terminal 86 Green/black, which goes to the module. This should energize the relay which is normally closed between terminal 30 and terminal 87 center to close between terminal 30 and terminal 87a. Once this closes (30, 87a) power goes from the R/Y 87a wire to Green/White and energizes the solenoid and starts the engine, Thus doing the same thing as jumping from the battery. Only problem is it doesn't work. There several things, actually many things I don't understand. I guessed that the Green/Black wire is a ground wire, only because it has black on the wire. If the module does not ground the ground wire the relay would not be energized and would not complete the circuit. Also on the back of the connection block which the relay is plugged into is a jumper wire with something small in the wire, is this a diode? This jumper wire goes from terminal 85 to 86. The rest of the story is, I just replace the battery, the battery has an identification mark on it 1u, so I bought a new battery with a 1u, but it also had an r on it. Put the battery in the holder hook up the terminals and try to start the engine, nothing happened. Then I noticed that the little had to see plus was on the right in stead of the left. The dummy had the battery was in backwards. Is is possible that had something to do with the jump (diode?) or the module? If my theory is correct why not go directly to the spade from the starter switch?