What to do when you car wont start

First, let's look at the obvious: the battery. When the battery is run down, but the headlights seem to shine at full strength, usually the starter makes click-click-click noises. That usually means you need a jump start. Of course, if the headlights are dim or off entirely, the battery is the most likely candidate.

A clicking noise from the starter indicates (usually) a dead or dying battery, and (sometimes) a dead starter. This may be a common problem on 3.3 family engines as they grow older. A single click from under the hood on an attempted start could mean a bad starter relay. Jump starts do not always work; poor quality cables can prevent enough power from being made.
If the battery's in fine fettle, there are a few other problems that could cause your car to refuse to start. First, check the gas.
One contributor noted (this relates to older cars, as newer ones do not have distributors or rotors):
A perfectly running, recently tuned car died and would not restart. It turned out to be the ignition rotor. The bad rotor was only a couple weeks old and looked perfect. There was spark at the spark plugs so that test alone is no indication. There were no codes set in the computer and I tested everything in the ignition and fuel system. I discovered it was the defective rotor, partly by luck.
It is impractical to carry all kinds of spare parts in your car, but carry at least a rotor ($8) and probably a cap ($10) as those are cheap and very easy to replace, under 5 minutes. Your rotor, no matter how new or perfect looking, can fail any time and leave you stranded, as it did to me. It is your $8 insurance against at least one reason why you might need a tow.
If you car is not starting or stalling and you are about to pull your hair out, try a new rotor and a new cap, even if the ones in the car are very recent. It just might do it, and it is a cheap fix.
This also emphasizes the need to really dig into the basics of ignition before proceeding with more exotic tests. In my case, cap, rotor and wires were brand new, but don't discount the possibility that some of those may be defective, even if they look perfect. Some tests can be unreliable and insufficient, as I learned from the spark plug test that looked okay despite the bad rotor. Next time you do your tune up, keep your old cap, rotor and wires, that you know are working, to try in case something is wrong and quickly eliminate many possibilities.
If the engine was wet, dry it, separate the wires, and try again, Use silicone spray or "wire drier" and, if that works, replace your wires with really good ones ($25-$60 mail order). Dan Stern recommended Whitaker's Multi-Mag, which look like the original wires, but uses the spiral-wound construction of modern, high performance wires: lower resistance, but no irritating radio noise. They have a lifetime guarantee and don't cost more than regular carbon-string type wires. The Slant-6 wire set (32605 for pre-1975) has the correct one-piece moulded plug boots. They are also sold under the Borg Warner/BWD KoolWire name.
Many have found that automatic-equipped cars would not start in Park, but will start in Neutral. Bill Watson suggested that the shifter linkage might be out of adjustment, very slightly.
The linkage from your steering column attaches to an "arm" that sticks out from the ****** on the driver's side (console shifters are similar). Get under the car while someone moves the gearshift linkage. This way you will be able to determine which way it goes when you put it into park.
What you do is place the car in park, loosen the bolts to the "arm", push the arm all the way in the direction park is engaged. Then push your gear level all the over the left - as far into "P" as it will go. Then tighten everything up.
The problem could also be the neutral safety switch, if it will not start at all:
To find the neutral safety switch, look for a small wire attached to your starter solenoid that leads down under the floor toward the transmission. You will find the neutral safety switch at the other end of it. [This switch may simply be dirty]. ... John Smith had starting problems, mostly when cold, on his 250,000 mile Dodge Spirit. He found oil in the neutral switch next to the transmission dipstick. Cleaning the connection seemed to fix it.