Why do I keep getting the "You can't sign in to iCloud at this time" messages?

I keep getting the message when TRYING to sign into my iCloud account while using the System Preferences or using the Mail app on the computer I am currently using.

HOWEVER:

I CAN sign into my Apple ID account using this Apple Support Community. Same Apple ID. Same password. Same computer.

I CAN sign into my Apple ID account using iTunes. Same Apple ID. Same computer.

I CAN sign into my Apple ID account using a browser. Same Apple ID. Same computer.

How can I FIX this problem using methods that I have NOT already tried?

Tried the following with no success.

1) Rebooting

2) Rebooting in Safe Mode

3) Logging out of User Account and then back in

4) Re-authorizing Computer using iTunes

5) Removing Computer using iCloud access via a browser (on the same computer).

6) Resetting my Keychain using the Keychain app (someone else suggested it, but this was STUPID; all it did was delete about 100 previously saved passwords)

7) Tried signing in with VPN turned off; VPN “on” or “off” does NOT affect being able to sign into iCloud using browser at <icloud.com> or into my Apple ID Account using iTunes.

I CAN see this computer using the Find My app on my phone.

EVERY time I TRY to sign in I get the same “You can’t sign in to iCloud at this time” message.

Please help!

Thanks.