I see you mentioned "VOLTAGE DROP" several times.... this is exactly why I suggested using voltmeter to take "Voltage Drop" measurements and it should take less than 10 minutes to isolate root cause.
Yes you did. And looking back on it, I think we are both guilty of using the term without adequately explaining the concept to the new people. So here goes:
If you google "Ohms Law", you will find an equation such as V=IR. This simply means that the Voltage Drop (V, measured in volts) between the two points measured in an electrical circuit is equal to the Current (I, measured in amps) times the Resistance (R, measured in ohms).
If you have a perfect conductor without any resistance then A amps x 0 ohms = 0 volts.. Similarly, if there is no current flowing then 0 amps x R ohms = 0 volts. There must be some current and some resistance to produce a measurable voltage drop.
Now at this point, some of you are saying "That can't be true -- the meter shows 12 volts when I measure the battery + to -." What you are actually measuring there is potential voltage -- the maximum voltage the battery can supply. The current is miniscule (a few microamps in a digital meter) but the resistance is infinite because the circuit is not yet a closed loop.
Turn something on and the battery voltage will drop. If you were to place a nice fat wrench across the battery terminals, you would see the voltage drop to near 0 (through the sparks, before the wrench turned red and melted) because now the resistance is near 0. Anything x 0 = 0.
EG: Battery voltage is 12.8v with everything off. Turn on the headlights so current flows and the voltage drops to, say, 12.5 volts. The sum of the resistances of the headlights, switch & wires times the current through the circuit equals 12.5 volts (current is always identical at all points in a closed circuit).
If we cranked the engine instead, we might expect to see a battery voltage of, say, 10 volts, because even though the current is much higher, the resistance of the starter motor and those big fat cables is much lower. If we
don't see a significant voltage drop it means we have high resistance somewhere.
This was the case in the OP's problem. He hit the key and the battery voltage did not drop. He measured from the starter + terminal to the battery ground and the voltage was near 0. If he had measured the voltage drop between the battery + and the starter while cranking, he would have found the missing 12v -- that is, his meter would show a voltage drop of 12v between the battery and the starter motor -- meaning high resistance in one of the cable, the solenoid or the connections. Metering between either side of the solenoid, he would have found near 0 volts. Metering between the battery + and the solenoid would confirm the voltage drop in the wire and connections was eating up the missing 12 volts.
But let us say he found a voltage drop of 0 between solenoid and battery +. He could then meter between the either side of the solenoid. 12v there means either the solenoid contacts or the switch circuit is at fault -- more on that in a moment. Moving on, check between starter + and the starter case. If it was still near 0, then between the starter case and the engine block. If that was still 0, then odds are he would find 12 v between engine block and battery -- ie bad engine ground or battery connection.
By measuring the voltage drop at all the significant points of the circuit, we can methodically isolate the source of high resistance.
Now, back to the solenoid: The solenoid is actually part of two independent circuits. Obviously it acts as a switch in the starter circuit itself. Burned contacts can be a source of high resistance in that circuit. But it is also part of the key switch circuit, which may include the clutch safety switch, etc. This is were a wiring diagram becomes invaluable, identifying all the various components in the circuit and maybe even their locations.
The solenoid itself should give a nice sharp "click" when the key is turned. If it does but the voltage drop across the solenoid contacts is high then probably the contacts are burnt. If there is no click, or it is an anemic little tick, then we use the same diagnostic process of checking voltage drop through that circuit, starting with the fuse(s), ignition switch, through each safety switch and so on.
Ok, finally: why not just use the meters Ohms scale to measure resistance directly? Well sometimes you can, if it is a low current circuit. But bear in mind that the meter is actually measuring resistance by measuring voltage drop -- the difference is the meter is supplying the potential voltage from it's tiny little AA or 9v battery, meaning it can only supply milliamps of current. Remember that V=IR -- little current means little voltage drop, even if resistance is high. So a poor connection that is capable of passing a tiny current may appear to have low resistance to your meter when in fact it just can't supply the current required under actual conditions.