Unplug the power cord from the game console and from the AC outlet. Failure to do so can result in electrical shock or death.
Set the multimeter to continuity test mode.
The setting is symbolized by a "volume indicator" as seen in the picture. If the meter is set to the correct mode, you should hear the meter beep when the leads are touched together.
Verify that the positive lead is plugged to the voltmeter/ ohmmeter outlet.
Test for a potential open circuit by using one multimeter lead to touch one of the prongs on the AC side of power cord. Use the other lead to touch one end of the console side of the power cord.
If there is an adequate electrical connection, the multimeter will beep. If it does not beep the first time, try using the lead to touch the other prong.
Repeat the above directions in step 2 for the other outlet and prong of the power cord.
If the multimeter fails to beep on any of the occasions outlined above, your power cord is open. In other words, you will need to replace the power cable.