Trouble With Starting Car

I recently bought a 1968 Cougar. The stock 302 was replaced with a 351 Windsor by the previous owner. The car also has electronic ignition, and a high performance ignition coil.
The starter cranks in the “run” position, but doesn’t crank when the key is turned to the “start” position. I’ve replaced the ignition switch and the starter solenoid, but I still haven’t been able to figure out this problem. The previous owner stated that he “never had this problem until he went to replace the ignition switch”. Some wires underneath the dashboard have been spliced.
So far, I’ve only tested the wire running to the “S” terminal on the starter solenoid, and the solenoid itself. I’m not sure if reversing the wires on the “S” and “I” terminals on the starter solenoid could cause this. Every once in a while, the starter solenoid gets stuck, causing the starter to crank until the battery is disconnected.
Does anyone have any suggestions as to what I should do, or what I should test? Thanks in advance.

Disconnect both small wires at the starter solenoid. When the key is in RUN, only the green/red or red/green wire will have voltage. When the key is in CRANK position, the red/blue wire will have voltage and the other will not. The green/red or red/green wire is the I wire; the blue/red wire is the S wire, located towards the radiator. The I wire is towards the starter or windshield.

This is from a '67, but should be similar.

Hope it helps:

Ignore purple wires on the right, the side slots and center post are key. The center post fires the starter, but some other things have to happen to close the starter relay and supply the coil (inside the IGN Switch), so the side connections are key.

#1)Yellow (first slot): Voltage Supply from Starter Relay (Battery side), comes from a trunk supplied by a black/yellow wire at the relay

#2)Red Blue (center slot): Energizes Starter Relay - connects to at Relay LEFT push terminal (may change to brown)

#3)Violet (wrinkled, center post): Voltage for Starter Motor…connects to at Starter Relay RIGHT push terminal (may change to brown or Green red) gets connected to Starter inside the relay when the relay closes from #2 getting voltage ( wire 904 listed as Green-Red )

#4)PINK-Resistor wire, connects to red-green wire going to coil (Last Slot, same as Red Yellow wire seen)

I am guessing, #2 and #4 reversed? Let us know.

Thanks for your replies!
Earlier today, I went outside and tested the wires running to the solenoid with a test light. The I wire got power when the ignition was turned to run, and turned off when the ignition switch was turned to start. The S wire got power in the start position, but not in the crank position. The solenoid clicked when the ignition switch was turned to the crank position. Everything seemed to have worked as it should (although the light was much brighter when testing the S wire). This is rather odd, as I haven’t worked on the car since I bought it. I checked the wires coming from the ignition switch, and all the wires are hooked up correctly.
I forgot to mention that just the ignition switch is hooked up. The lock cylinder isn’t attached. Is there a trick to installing the lock cylinder? I’ve tried installing it myself, and took it to three local mechanics, none of which were able to get the lock cylinder to stay in the ignition switch. Could a missing lock cylinder cause issues with power running to the solenoid wires? Thanks in advance.

[quote=“67ClassicCougar”]Thanks for your replies!
Earlier today, I went outside and tested the wires running to the solenoid with a test light. The I wire got power when the ignition was turned to run, and turned off when the ignition switch was turned to start. The S wire got power in the start position, but not in the crank position. The solenoid clicked when the ignition switch was turned to the crank position. /quote]

Let’s call the three basic ignition key positions OFF, Run, Crank.
The I wire should have power only when the key is in the RUN position (assuming it is disconnected from the starter solenoid).
The S wire should have power only when the key is in the CRANK position.

Not having a lock cylinder in the ignition switch is not the best thing for the car. I once had mine fail, removed it, and the battery died due to a large current draw somehow. I know this doesn’t make sense (I probably mis-remember the sequence of events), but without a lock cylinder, it should be OK. Just to be safe, I would disconnect the battery until you have that problem resolved.

It sounds like you have the I and S wires at the relay reversed. Left-center terminal is ‘S’, Right-Center is ‘I’

Hot wire by running jumper direct to coil from battery, and jump another wire to touch starter relay output (far right big terminal) and hot wire.

The I wire stills need power during the crank, but it is provided by the Starter relay on the 262 wire from the I terminal ONLY during cranking, then the ignition switch supplies it in the run pos.

Whoops. Looks like I made a typo. Sorry about that. I meant to say that the I wire got power in the run position, but not in the crank position. The S wire got power in the crank position, but not in the run position. I also tested the terminal of the solenoid that the starter wire attaches to. It got power in crank, but not run. Strangely, it seems to be working normally now, even though I haven’t done anything to the car yet.