120819-1502 EDT
Get a three wire extension cord from a known working power outlet, and bring the extension cord socket to the kitchen area. Create a 25 W and a 15 W incandescent test light. Also have a high impedance DVM.
Connect one side of the 15 W test lamp to the extension cord hot wire. The other side of the bulb use as a test probe. See if the bulb lights when connected to the neutral of each receptacle. If it lights at full brightness at each outlet, then the neutral is probably connected back to the main panel. If the bulb got very bright and burned out, then neutral is probably connected to a 120 V leg of opposite phase to your extension cord hot wire. If the test light does not light, then the neutral is open going back to the main panel, or it is at 120 V of the same phase as your extension cord.
Next pick one of the non-working receptacles and connect the DVM in AC Volts range between hot and neutral. The voltage should be near zero or not very large. Also test the voltage from the extension cord neutral to hot, neutral, and EGC of the dead circuit. If there is some voltage, then put the 25 W lamp load on the socket between hot and neutral. Now the voltage should be zero. Assuming this is the case, then connect the 15 W test lamp test wire to the hot slot of one of the outlets. Both bulbs should glow dim. There will be about 35 V across the 25 W and 85 V across the 15 W if the source is 120 V.
This provides a voltage divider between the extension cord hot and the outlet neutrals. The divided voltage will be between the outlets hot slot and neutral. Check that the same voltage exists between the hot and neutral slots of each outlet.
Use the 15 W test bulb to test each EGC slot of each outlet. The bulb should be full brightness.
If all these tests check out, then it points to an open in the hot side somewhere.
If some of the tests above failed, then you need to find out why. Suppose the test light did not glow full brightness when connected to the neutral. Is the neutral open, or is it connected to a 120 V leg instead of neutral?
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