First, I am not an electrician so bear with me. I just got the motor/transmission installed. Along with radiator battery, etc. Hooked everything up & turned the key & nothing. When I say nothing I mean nothing, no click, nothing. Checked the battery: 12+ v. I can jump from S1 to the positive terminal on the starter solenoid & it will turn over. So I pulled the ignition switch & got the following: When you key is off: The center post has 0v. The red/blue wire has 0v. The red/yellow & brown wires have 0v. The Yellow wire has 12+ v. When I turn the key ON, the the center post has 12+ v, the red/yellow & brown wires have 12+ v, the yellow wire has 12+ v, the red/blue wire has 0v. When I turn the key to the start position, then the red/blue wire also has 12+ v. So in the start position all of the connections on the ignition switch have 12+ volts. Still nothing. I have changed the starter solenoid & still nothing. Is it possible that the Regulator might be bad? Any insight anyone can provide would be greatly appreciated. 
Additional info: There are no door jam switches installed, there is no steering column installed & I disconnect the neutral safety switch since I need to check that it is actually in Park.
What year cougar?
Early 67
Did you bypass the neutral safety switch or just unplug it from the transmission?
Start with the easy part, is the wire on the S terminal red/ blue, it should be, if it is ,check for voltage with key in start position, if voltage is there then you have a bad relay
Oh, Dave is right, the neutral switch needs to be jumpered out to complete the circuit.
The neutral safety switch was just unplugged from the connection at the firewall. How do I jumper it?
With the key in the Start position I get 0 volts at S.
Also, my neutral safety switch has two connectors.
I believe you need to jumper the two red w/blue stripe.
So I disconnected the connector at the Voltage Regulator & measured the voltage on the wire that connects to the ‘I’ terminal on the voltage regulator. With the key off, 0 volts. With the key ON, 12+ volts. With the key in the start position, it drops down to almost 0 volts.
You guys are freaking GENIUSES. I jumper-ed the two red/blue wires on the connector that runs into the car (where the neutral safety switch wires connect) & it turned right over. You all deserve a beer for this one. 
It also proves that although the floor shifter is in Park, the transmission is not.
Glad I could help. The next time I’m in your neck of the woods, I’ll collect on that beer.
Knew it was too easy. With the key in the ON position it tries to start. With the key is the Start position nothing happens. Either the ignition switch is bad or I have something crossed. Help again Please.
The S terminal should have red w/blue wire on it and the I terminal should have a brown wire on it.
Confirmed. That is how they are hooked up.
Earlier when I disconnected the connector at the Voltage Regulator & measured the voltage on the wire that connects to the ‘I’ terminal on the voltage regulator, With the key off, 0 volts. With the key ON, 12+ volts. With the key in the start position, it drops down to almost 0 volts. Thinking maybe either ignition switch or maybe the connector/wiring that connects to the ignition switch may need some work.
You need to jumper the two red/blue wires coming out of the firewall grommet in the 4 pin plug: male to female. This simulates the neutral safety switch being in park or neutral, which jumpers those two wires. Without that jumper, you will not get any voltage to the S terminal on the starter solenoid.