My car will not start by turning the key to ignition. It is a '68 302 4v j automatic. I replaced the starter a few months ago, replaced the cylinoid in the engine bay, and the ignition switch. I can start the car by using two screwdrivers crossing from the sides of the cylinoid with the key in the on position. So first thought was the cylinoid. replaced it. didnt fix it. next replaced ignition switch. still no good. i even just bought the 70$ neutral safety switch and thought for sure that could be the last possible thing wrong with it! Why wont my car start?! 
Is your car an XR7? If so, try temporarily bypassing the tachometer.
Did you replace the ing.switch, starter and solenoid all at the same time,…from a previous problem with the same symptoms? The made in ??? solenoids are not know for there quality. Did the car run well in the past and did this starting problem evolve or happen overnight? If you are able to jump it across the solenoid and it starts and runs…sounds like a wiring problem with the start momentary sending power to the solenoid…oversimplified, but start a power continuity test on the back connector of the ing. switch and trace the wires to their contact points. Then there’s always a qualified auto elec. tech. to relieve you of your woes and cash!
It is not an xr7 and it stopped starting out of no where. So i tried the jumping across the solenoid and it worked, so i assumed that the solenoid must have been bad since i had heard they often are a problem on this vehicle. That didnt fix it so then i tried the ignition switch replacing, then that didnt work so i tried the neutral switch.
Try the red w/blue stripe wire coming from the back of the ign.switch, it connects to the front side of the solenoid. See if it relays power to the solenoid with the ign. switch in the start position. So, have someone hold the key on and you check the wire, at the solenoid, for volts DC.
Won’t start?
Engine won’t spin over or will spin and won’t start?
wont spin
Do you have tilt away steering?
i have tilt up and down but if it has tilt away i never got that to work
I thought that might be the case. There is a second starter safety switch that won’t let the car start if the tilt away feature is triggered. You probably opened the door with the engine running and it made just enough vacuum at the release vacuum motor to allow the switch to open. In '68 the switch is built inside the vacuum motor. You may be able to just pull the release cable coming out of the vacuum motor back to locked position and get the switch to make contact again. Other wise, you may need to disassemble the vacuum motor, and clean the switch contacts. Be careful this is an expensive part.
My 68 did the same thing when I first got it. Try pulling down on the steering wheel as you turn the key and see if it starts. Or pull on the cable itself as you turn the key. If that works, you may just need to adjust the tension on the cable. The bracket holding the cable for the tilt away is slotted to allow for adjustment. Who knows, you may fix two problems at the same time).
I looked under the column and there is a black motor looking thing with a metal cable coming out of it allowing the cable to pull out some or go in. the cable is snapped, and there is a red and blue wire near there that is looped back into its self with a home made loop. It looks as though the previous owners bypassed this little black cylinder.
The real way to fix this is to follow the circuit path with a volt meter and find out where the circuit is broken. I think that that is where you are at now that you have found previous owners have messed things up.
I have current from the solenoid to the ignition switch, then from the switch to the connection for the neutral safety switch but i am not sure if it is coming back from the switch or not. but i cant start the car by trying to bypass the safety switch so i think that should rule out the safety switch especially since i just replaced the neutral safety switch.
There are too many “switches” in your description…ignition, neutral safety or tilt-away. Are you getting between 9.5-13.5 volts DC at the S terminal (red w/blue stripe wire) on the solenoid with the key turned and held to the start position?
Finally she is running. The issue was the solenoid. I replaced that first in the journey of trying to find the issue. But I found out sometimes the solenoid has an infant death and can be no good at purchase. I got another solenoid and now the car turns over like a champ. Thanks for all the help you guys bring to light many insightful ideas of what could be wrong. Thank all of you for being here to help with the car troubles, I’m sure I will be posting again soon with an issue. 
Congrats on getting things up and running. …and getting your tilt away diagnosed as part of the bargain.
Rather than start a new thread to ask a similar question I’m piggybacking here
Today as I was backing my car into my driveway, the engine died. Tach is already bypassed from when it died not long ago.
Car wouldn’t turn over, was acting like it had a dead battery though I haven’t had battery issues and had just started her off the battery twice in like a half hour, to go run an errand and then return home.
Here’s where it gets interesting.
Just now, with my wife’s car home, I went to try jumping the cougar to see if it was a battery issue. Before hooking up the jumper cables, I was getting interior lights, a fraction of a crank when I turned the key, then silence, then interior lights fading back in. Seemed like a dead battery.
After running the wife’s car for a bit to charge up the cougar’s battery I tried again. This time, a fraction of a crank, interior lights dimming, then I switched the key back to the off position, but the starter tried again, cranked a little, then kept trying, cranking and eventually getting the engine started, ALL WITH THE KEY REMOVED, and reached a point where the engine was firing but the starter was still cranking. To get it to stop I had to run to the front of the car and disconnect the jumper cables.
So is this a malfunctioning starter solenoid? That will be a little annoying since it’s less than a year old, but also not bad since it’s an easy fix.
That was really freaking me out, the car starting with no key.
Sounds like you have a bad ignition switch then…
Is your wife’s car a Toyota? It could be that the unintended acceleration demon’s spirit passed through the jumper cables into your cougar seeking to possess it, kill you and steal your soul. Or it’s the ignition switch like suggested above.