Look for another identifier besides color such as a stripe or rib on one of the two other wires. That will be the Neutral wire. Make sure it connects to the Wide blade on the plug.

Is this because it is AC? No, if it isn't so identified, you are dealing with a cheap knockoff pigtail that probably belongs in the waste bin. In the 120V single phase world, Neutral is effectively at ground potential, therefore if you touch it, you shouldn't get shocked. Hot while alternating isn't at ground potential and so the voltage is alternating between +120V and -120V (RMS, actual voltage peak ±170V), making you the conductor if you connect the hot wire to the dishwasher chassis and you touch it and ground. If the neutral connects to ground in the dishwasher, you've just connected up a dead short.

As this is for a dishwasher, neutral must connect to neutral and hot to hot, any mess-up here is going to be ugly. The only other method is to use an ohmmeter to trace which wire is attached to which blade. Normally narrow blade hot, wide blade neutral and ground pin to ground. If there is no difference in blade widths, then use the socket chart below to figure out which blade is Hot and Neutral from its position and attach the wire to the appropriate terminal in the appliance.

There is only one instance where the connections could be considered even remotely "interchangeable" and that is on a double insulated device where neutral is totally and completely isolated from ground.

NEMA socket listing with blade width and "polarity". Note that NEMA 5-15 and 5-20 can be installed with the ground prong up (coat hanger excluder mode) so right and left slot position is relative.

National Electrical Code 2014

Chapter 4 Equipment for General Use

Article 400 Flexible Cords and Cables

II. Construction Specifications

400.22 Grounded-Conductor Identification. One conductor of flexible cords that is intended to be used as a grounded circuit conductor shall have a continuous marker that readily distinguishes it from the other conductor or conductors. The identification shall consist of one of the methods indicated in 400.22(A) through (F).

(A) Colored Braid. A braid finished to show a white or gray color and the braid on the other conductor or conductors finished to show a readily distinguishable solid color or colors.

(B) Tracer in Braid. A tracer in a braid of any color contrasting with that of the braid and no tracer in the braid of the other conductor or conductors. No tracer shall be used in the braid of any conductor of a flexible cord that contains a conductor having a braid finished to show white or gray.

(C) Colored Insulation. A white or gray insulation on one conductor and insulation of a readily distinguishable color or colors on the other conductor or conductors for cords having no braids on the individual conductors. For jacketed cords furnished with appliances, one conductor having its insulation colored light blue, with the other conductors having their insulation of a readily distinguishable color other than white or gray.

(D) Colored Separator. A white or gray separator on one conductor and a separator of a readily distinguishable solid color on the other conductor or conductors of cords having insulation on the individual conductors integral with the jacket.

(E) Tinned Conductors. One conductor having the individual strands tinned and the other conductor or conductors having the individual strands untinned for cords having insulation on the individual conductors integral with the jacket.

(F) Surface Marking. One or more ridges, grooves, or white stripes located on the exterior of the cord so as to identify one conductor for cords having insulation on the individual conductors integral with the jacket.

Since there's no grounding conductor in the box (i.e. the box is not grounded), touching a meter lead to metal is basically useless.Your COM probe should go to the grounded (neutral) (white wire in your case), then you can use the other probe to test for voltage.

It sounds to me like there might be a problem with the wiring inside the fixture, since you said the light kit on its own worked. It sounds like for some reason either the blue or the white wires are not continuous through the fixture to the light kit. Maybe a loose or bad connection inside the unit, or a loose or bad connection where the light kit clips into the fan.

If your multi-meter has a continuity setting, you could use that to test the continuity through to the light kit. If not, you can use the resistance feature to do the testing.

The continuity setting will look something like this...

While the resistance setting will be represented by the omega symbol (Ω). If you're using the resistance settings, you'll want to use the lowest setting (usually 200, 400, or similar).

Testing continuity

• Turn the power off to the fixture using the circuit breaker, and verify power is off.
• Disconnect the white and blue wires from the building wiring.
• With the light kit disconnected from the fan.
  • touch one probe to the white wire at the top of the fan, and the other to the white wire where the light kit should connect. Note the reading.
  • touch one probe to the blue wire at the top of the fan, and the other to the blue wire where the light kit should connect. Note the reading.
  • touch one probe to the white wire of the light kit, and the other to the threaded bit in the light socket. Note the reading.
  • touch one probe to the blue wire of the light kit, and the other to the contact at the bottom of the light socket. Note the reading.
• With the light kit connected to the fan.
  • touch one probe to the white wire at the top of the fan, and the other to the threaded bit in the light socket. Note the reading.
  • touch one probe to the blue wire at the top of the fan, and the other to the contact at the bottom of the light socket. Note the reading.

When testing continuity, a beep or low resistance reading means there's electrical continuity between the two test points (i.e. electricity can flow between the points). If there's no beep, or an open or infinite reading, it means there's no electrical continuity (i.e. electricity cannot flow between the two points). If there's a high resistance reading, it means that there's a bad connection between the two points (i.e. electricity cannot flow easily between the two points).

If the continuity tests all pass (i.e. there's continuity from the top of the fan through to the socket), then you'll want to check the bulbs to make sure they're good, and check the contacts within the sockets to make sure they are making solid contact with the bulb.

If it still doesn't work, you'll want to think about exchanging the fixture.