Starting problem

Concerning a 2002 buick century with about 52, 000 miles: About 8 months ago, the car wouldn?t start: battery was ok -lights would go on -no clicking noise -just nothing. Had the car towed about 20 miles to a GM dealer, and when the car was unloaded, it started fine. Left the car there for about a week, dealer tried several times a day to start the car, and it started ok each time. Dealer puzzled, switched a couple of gizmos in the computer system, without any result: said to use a different ignition key, which I have been doing. Drove on home, car worked fine for next couple of months, then same thing happened -car just wouldn?t start. Had it towed again, and same thing happened -when it got to the shop, started without a problem. Mechanic shined up the cable to the starter and suggested if it happens again, jiggle the shift lever up and down, jiggle the steering column up and down. Drove home again, and in another couple months, did it again. Jiggled the gear lever and the steering column without any IMMEDIATE result. That was a Saturday afternoon, so couldn?t call the repair shop so that they could come and see what was going on. Got ready to walk, gave the thing one final chance by turning the key, and it started. Mechanic puzzled -says it could be in the key, or the starter, could be something in the steering column, could be something in the transmission - but no telling what. Any help ?

The obvious cause would be an erratic neutral safety switch. Have they not considered this?
When it won’t start shift into neutral and try it. If it starts then you know that is the problem.

Another less likely causes could be the electrical part of the ignition switch or a security system fault if the car is equipped with this.
“Shining the shift cable” is a good one.

When any circuit doesn’t work sometime, the circuit should be energized (key turned ON) many times until a particular section of the (START, etc) circuit shows a fault. For example: disconnect the START circuit wire at the starter solenoid. Touch the voltmeter positive lead to the disconnected wire terminal. Have helper turn the ignition to START, and OFF, START and OFF until it misses to send the 12 volts. Then, the voltmeter probe is moved one device (switch, etc.) closer to the ignition switch, and START and Off multiple times until voltage fails. When voltage doesn’t fail, the device (switch) that was just previouly checked (lost voltage), is the defective one.

I appreciate very much the suggestion re the neutral safety switch -that has not been mentioned, and I will ask about it. Usually, when I start the car, the shift lever is in the park position.
I’m obviously not a mechanic,and so when I spoke of 'shining up’something, I should have said that I understood that the mechanic had checked the cable to the starter to see if there was any corrosion -and had 'shined it up’to remove any possible traces of such.
Again,many thanx for your reply

The OP said he wasn’t a mechanic but maybe he should show your post to whoever works on the car- if he can convince the tech it makes sense.

What surprises me about this is that apparently nobody working on the car has considered the neutral safety switch. That’s always the prime suspect whenver a starter solenoid will not click when the key is turned to the START position.

Granted, a test may be inconclusive if the vehicle is starting every time but one would have thought that someone would have suggested the neutral switch by this point.

Next time it acts up shift gently into neutral and then try to start it.

I’m not really surprised to note that no one (mechanic, whomever) has an electrical troubleshooting technique, nor, knows how to read an electrical wiring diagram, nor, reads the repair manuals. If my impression is wrong, they can prove it by fixing this problem. Is there no teaching, or learning, in this half of vehicle maintenance? Yes, these start circuits are more complicated than on many other vehicles: 1. ignition switch, 2. PCM, 3. starter relay, 4. P/N switch, 5. starter hold-in coil, 6. four, or five, fuses, 7. Two wiring circuits. This may be a “three-mechanic” job: one to read the wiring schematic, a second to manipulate the digital multimeter, and a third to operate the ignition switch.