You need to do the following readings:
Ground = directly connected to battery's -ve terminal
+Lead = the +ve lead from your multimeter
1. Resting voltage: ignition off, key's in the OFF position (or out), +Lead on battery's +ve terminal.
2. Battery drain: Same as #1, but key's in the ON position.
3a. Same as #2, ignition key is in the ON position; But, the +Lead is on the solenoid's "HOT" terminal --- this is directly connected to the battery's +ve terminal. It should be obvious, since it's the only terminal that will have a voltage reading. ie. the solenoid only has two terminals, if one shows no voltage reading, then the other terminal is the "HOT" one.
3b. Same as #3a, ignition key is in the ON position; But the +Lead is on the solenoid's NON-"HOT" terminal.
4. Same as #3b, igntion key is in the ON position; +Lead is on the solenoid's NON-"HOT" terminal. And, activate the Starter Button.
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#1, Depending on your battery, and its condition should, generally be > 12.5V. If not, your battery is suspect.
#2, If this reading is significantly different than #1, say a difference of > 1.0V, then there's a "drain" or short in the system. Or, your battery is no longer able to sustain a load, and the reading from #1 is simply a surface charge.
#3a, Should be the same as #2. If not, there's a problem with the wiring b/n the solenoid and the battery.
#3b, Should be 0.0v. If not, the solenoid is bad.
#4, Should be close to reading from #2. If not, the solenoid is bad.
If you've checked all of the above, and the starter still won't engage. It's the wiring to the starter, or the starter itself.
Hope this helps.
