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What that small settings change would be, depends upon what the details of your WiFi setup are.
Some details that you might have to enable, and disable, on your WiFi router, are listed on this page:
The most likely to be crucial are, you need to be using the 2.4 GHz radio frequency band, and you need to have UPnP and IGMP enabled. And some other things disabled.
Since it only says that after you enter your WiFi passcode or passphrase, you may need to alter the passphrase you have chosen a little. Or, you may not be observing the difference between UPPER CASE and lower case letters, in that passphrase. The case of letters is important, and if you entered a passphrase of ErtyUiop2345 (not a good passphrase, but an example) into your WiFi router to begin with, then you must enter ErtyUiop2345 into the ChromeCast setup, also, exact like that, and not ERTYUIOP2345 nor ertyuiop2345.
Also, the encryption scheme is important - it is basically either 'open' or without encryption and without passphrase, or else it uses WEP-64 (not a good choice) or WEP-128, or WPA of several sorts. I'm not sure what encryption scheme you chose, but it might matter to the setup of ChromeCast.
Don't let me know your passphrase! I just need to know what your WiFi encryption scheme is, perhaps.