@Zachary Cole
Have you tried to [https://www.quora.com/How-do-you-reset-a-KitchenAid-dishwasher-that-wont-start|reset] the dishwasher, just in case it has glitched somehow? Worth a try and nothing lost if it doesn't work except a few minutes of time ;-)
If still no good hopefully it may be something simple like a faulty connection etc.
Check the wire colour at the solenoid and then find the same colour at the control board connector (maybe there aren't too many the same colour).
First prove continuity from the control board to the solenoid and if OK then trace the circuit back on the board to find where the power comes from for the solenoid.
I realize that you measured a small DC voltage at the solenoid, but this could be a spurious measurement as there may be feedback paths given that one wire connected to the solenoid is connected to the neutral mains (Line 2?) side of the power supply as the solenoid is powered by AC, and this wire connects to a lot of other parts in the circuit e.g. heater, circulation pump etc and through them back to the control board.
The solenoid operate wire is from the control board. The other wire is the return path i.e. the neutral mains wire. Not sure of the terminology where you are but here for AC power it is Active, Neutral and Earth and I think where you may be it is L1, L2 and Earth (if you have an Earth at the outlet as well) and the L2 wire is the return current path for the power. L1 being the active supply voltage wire
On the control board it may be a relay or a solid state switch (Triac) I don't know which, that the power is switched through to operate the solenoid but still worth a look.
Good luck and thanks for the feedback about the voltage.
Cheers