I have a '07 fit with 280 000km (175 000mi) and it recently has started to exhibit a delay when starting the engine. When I turn the key, there is a pause of about half a second before the engine starts cranking. Once it starts cranking, the sound/speed/strength of the cranking is just like new and the car has no trouble starting. I'm not talking about a slow crank - I'm talking about a pause before the cranking sequence begins after the key has been turned.

This happens in all weather conditions and all fuel levels. The car has no other known issues.

 

Is there any noise during this lag?

If you hear a soft whirring noise, I would guess that the Benedix mechanism on the starter motor may be sticking.

If there's no noise, it still might be some problem with the starter, or it could be any of a bunch of possible electrical-related problems: loose connection at the key switch, misadjusted or failing clutch pedal safety switch (if a manual) or park/neutral switch (if an automatic), loose wire to the starter solenoid, among others. It might be good to check the brushes on the starter motor, too; if it's like some and has four brushes, a single brush not making contact would reduce it's power by 50% and quite possibly make it marginal at cranking over the first compression stroke (before the engine has much momentum to carry it through).

It could conceivably also be a poor electrical connection or a misaligned safety switch (clutch or park/neutral, depending on the type of transmission), but I would generally expect those to be less consistent in working or not working.

 

If you hear relay buzz from driver side under dash fuse box, the problem likely is ignition switch. I have this issue once in a year; the starter typically operates at second try.
No sound at all or lag can be also caused by brushes not making contact with armature commutator (the pull in coil is connected in series with an armature and its total resistance is SMALLER than of hold-in solenoid coil connected in parallel)

 

No there is no noise or reaction whatsoever. The problem is worse now. When I turn the key, nothing happens at all unless I wiggle the key back and forth inside the house, then the engine will start.

 

Verify that battery is good.
If so, you have to test starter switch. This requires opening of the steering column cover and attaching starter remote switch (push button with 2 alligator clips) to the starter and power feed wire. If starter cranks with push button, but not with key , the ign switch needs replacement. if no cranking in both cases the starter or neutral start switch may need inspection.