[slob]

as per Post #10 in the link, the voltage should drop while the starter motor is connected by the solenoid, then recover quickly.
This does suggest a problem with the solenoid or cable/connection between solenoid and starter motor.
If you clip your multimeter + to the stud on the starter motor and - to a good earth, you should see ~12v on the meter when you press the button.

edit: or you have no connection between the battery pos. terminal and the high current side of the solenoid!