Mac: authentication of Apple ID fails

my Apple ID cannot be authenticated for iTunes, iCloud, calendar, contacts. (Calendar has the triangle icon with an exclamation mark. Contacts has the circle with the wavy line.)

when i try to sign-in, i get the error message "There was an error connecting to the Apple ID server."

Using another macbook, i was able to sign-in. (same wifi network, same router, same home internet connection.)

using Chrome, i am able to log-in to icloud.com.

from the console, i get the error messages:

akd Authentication with server failed! Error: <private>

akd Server auth response did not contain CK.

akd Server auth response did not contain PRK.

i changed the password of my Apple ID. i still cannot sign-in on my Macbook.

i tried changing the DNS server on my router. i still cannot sign-in.

i am able to sign-in to icloud on my iPhone6/iOS 10.2.1 and iPad Air/iOS 10.2.2 on the same wifi network, router, internet connection.

i do not have any anti-virus or anti-malware apps on my mac.

i tried disabling the firewall of my router. no effect.

i do not have any Certificates on this Macbook.

apple macbook air (Early 2015)

macOS Sierra 10.12.2