Wherever the problem is, it is a safe bet to assume that it is related to corroded electrical connections somewhere.

Since you have not yet narrowed the problem to fuel or spark, give us a few more clues (i.e. how does it run once it finally starts?) and start with the easiest thing to check.

Check to make sure that you have a hot blue spark while cranking the engines. Remove a spark plug, plug the wire back on, lay the plug where it gets a good ground to the threaded part. Tie/clamp it down if necessary. Crank the engine while someone watches the plug. The empty plug hole will whistle loudly if the car starts. Tell your neighbors to hush up and go back to sleep.

Hot blue spark while cranking? That's good. Start looking for fuel delivery problems. That's a subject for another post.

Weak yellow spark? You are probably on the right track.

While the plug is out, look at the center electrode. Assuming that it is a conventional plug, is the center pin still nice and square-edged, or have the edges of the pin rounded down? Spark likes to jump from/to sharp edges. Replacing worn plugs with fresh plugs will reduce the symptoms of a weak spark, though it won't solve the underlying problem. Most folks use Bosch, Denso, or NGK plugs. Conventional style plugs are fine. The fancy ($6+ each) plugs don't seem to be worth the extra money from my experience.

While you are under the hood, unplug and reconnect every electrical connector you see to freshen up the contacts. Watch how the releases work, and pull on the connector, not the wires. If you see a ground wire bolted to the engine or frame, remove it, clean it, and replace it. If you have not done this for a few years, it is time well spent.

If the spark is weak, look at your plug wires and distributor cap. If they are 10 years old or older, I would replace the wires, cap, and rotor before spending any more time diagnosing.