I cannot find any info on the given model number.

Since you have 120 volts across the motor and it does not run, I would say it is toast.

I cannot find info on this unit so the following is just what is usual.

[COLOR="Blue"]What tells the motor its time to run?[/COLOR]
The timer or the control board.

[COLOR="Blue"]I don't know if this is going to make sense, but I thought that the motor would have voltage to it all the time, and when it was signaled to run it would run. [/COLOR]
No the timer or control board completes the circuit to the motor (applies 120 volts) and then it runs.
[COLOR="Blue"]
Does the timer contain all the circuitry/logic for the dishwasher to run?[/COLOR]
Yes.
Often there is also a keyboard which inputs your selections into the control board.

[COLOR="Blue"]The motor performs all the functions of draining, filling and washing?[/COLOR]
Depends on the unit.
Some units have a separate wash pump and a drain pump.
Some units use the same pump for both washing and draining.

[COLOR="Blue"]What tells the heating element its time to dry?[/COLOR]
The timer or control board.

The door switch seems to be fine. With the switch open, no voltage is present at the motor or any of the other connections, and the opposite when closed.

Its a portable DW, so where is the terminal box at? Now that I know that the motor isn't signaled to turn on, it seems like the motor is the culprit here.

You need to check if you have 120v at the motor across neutral and not ground. Are any functions working (filling,indicator lights ect) If not check your power cord for continuity on the neutral side

Where the power cord connects to the dw; the connectors neutral terminal is blackened, like its been arching. Why I don't know, maybe just normal wear and tear? It looks like if I replace those connectors, everything should be ok. I'll splice the wires together instead and everything should work out fine.