No there is no change in the voltage when clamping the tester leads to the terminals and pushing the start/stop button.
That makes sense to me as you really are not creating a drain.. You are not cranking the motor, thus no drain...
Ok,,,
Lets take a step back here.
If you have a GOOD battery, GOOD wires and connections, GOOD starter, then it will crank if you jump the solenoid (assuming the engine is not seized).
If it does not crank, you have an issue with volts/amps. Period !!!!
So lets figure this out.
Have you removed and cleaned the large red and black wires?
Did you remove the wire from the starter to clean and inspect?
Did you remove the ground at the starter to clean and inspect?
There is a small wire that ground the solenoid. If this wire failed, then you will have a no start issue. Check this wire for continuity and ensure it is in fact grounded.
Take a set of jumper cables and, using the battery in the ski (as this will tell us if it really is a good battery), connect the hot lead to the output wire of the solenoid (it runs directly to the starter). It is best if you can connect to the starter but that is challenging. Take the other hot lead to the hot terminal. It should crank as the battery is grounded and the starter is grounded. If it does not, then connect the ground wire from the battery to the motor.
Let us know what you get...