There won't be any 120v power to the solenoid except when the ice maker controller opens the valve to add water, a duration of about 7 seconds in each 1.5-2.0 hour ice-making cycle. Hard to catch it. However, the 1402 manual has a section on winterizing the ice maker that tells how to manually trigger the solenoid.
Unlike the Norcolds, the Dometic NDA 1402 has only a single 120v power plug that supplies 120v to both the cooling unit electric heater and the ice maker. The 120v power flows via the control board 120v terminals, so maybe something got damaged there. That's the only connection I can think of. I now see that the NDA 1402 also has two power cords, one for the fridge and one for the ice maker. See Jeff's reply about the power to the plug used by the ice maker.
NOTE: See my later message about different versions of this fridge - there was a design change that affects ice maker operation:
http://www.rvforum.net/SMF_forum/index.php/topic,82973.msg752183.html#msg752183
Let's talk more about the ice maker symptoms. Is the bail arm on the ice maker fully down to allow it to start an ice cycle? Does the ice maker fill with water? If yes, did the water freeze?