Number ONE, I've never been able to look at a wire/connection and tell if it's good or not. A good DVM is a must have to isolate the problem.
Number TWO. When you have a good DVM, always work from a known good point to an unknown and always make voltage checks with the circuit under a load. So, I would recommend you follow the following procedure.
Connect the DVM across the two lead post on the battery, Should read 12.6VDC or greater. Then turn the switch to the cranking position, still should be 12.6 or greater unless the starter engages and tries cranking the motor. Anything below 10.6VDC is probably not going to let it crank..
If it stays at battery voltage and does not drop, start chasing it to where you loose it. The next check is to move the positive test lead to the small terminal on the starter solenoid. There are usually two, but the one nearest the battery cable is the positive. Turn key to cranking position and see if you are getting battery voltage. If you get battery voltage, the key switch is good. Now put it on the other small terminal and try it again. If you get battery voltage again, that means you are not getting a ground. One of those small terminals has to be grounded for the solenoid to work and if both have battery voltage when trying to crank it, there is no ground. If one has battery voltage and one doesn't when trying to crank it, the solenoid should be energizing.
Next step, If the voltage is dropping way down during the first test, leaving the meters negative cable on the negative battery post, connect the meters positive cable to the large terminal on the solenoid stud the battery cable connects to. You should be reading battery volts. Try cranking it with the key, the voltage should still hold battery voltage if the motors does not try to crank. If the voltages drops way down, you have a bad connection between in the cable between the battery and the solenoid. If it has battery voltage when trying to crank it, we need to check the ground cable.
Connect the meters positive cable back to the lead post on the battery and make sure it's reading battery voltage. Now more the meters negative cable from the negative battery post to the engines aluminum block or starter housing. You should still have battery voltage. Now trying cranking the motor with the key switch. It should still hold battery voltage unless the motor tries to crank. If it drops way down, you have a bad cable/connection between the battery and when the ground connects onto the motor.
To summarize,
The first test was to ensure you are getting 12VDC to and through the key switch to the starter solenoid. If you are, there is nothing with the controls that would keep it from cranking.
If you are not, the next text was to check battery connections.
So, next you checked the positive cable to make sure it was making good connection.
Then you checked the negative cable to make sure it was making good connection.
One of these three checks should identify where you problem is.
Now, if the battery cable connections test good, and the starter solenoid is not getting 12VDC when you try to crank it. Then you have a problem with the 12VDC lead going from the engine to the key switch or the key switch itself. This requires access to the back of the switch and a wiring diagram of the switch. Check the voltage between the battery negative and the battery terminal on the switch for battery voltage, you should have full battery voltage there. If not, find why you are not getting it there. If you are getting B+ to the battery terminal on the switch, turn switch on an make sure it's getting ignition voltage. Then try to crank checking the starter terminal and make sure it's sending B+ to solenoid.