Unable to sign in with my Apple ID on MacBook - No Error Message

jazzsir wrote:

The WiFi is connected (If the password is incorrect, an error window will appear.)

Your Mac is not connecting with iCloud server. Maybe resetting the router might help (it did for me). Also, rebooting your Mac would help too.

Also, have look here, If you can't connect or sign in to iCloud - Apple Support

Then, check if the wifi is connected.

If your email is correct, then the password is most probably wrong. Try again.

jazzsir wrote:

How do I reset my router? I can log in to icloud.com in browsers (Chrome, Safari).

If you can log in to browsers, your internet is working. There's no need to reset your router. But, the most simple way of resetting the router is by shutting it off, waiting ~10 seconds and rebooting it. As you can log in to iCloud from a browser, check if your password is correct. You can find your password in Safari Settings > Passwords, if you don't have it written somewhere else. You can then log out of your iCloud and log in again with that password in a browser that doesn't have it saved to check if it is correct.