It sounds like your FaceTime calls are failing to connect whether the call is made to you, or from you. I do'nt know if you have tried these steps, but I would use these steps from the article named:
FaceTime for Mac: Troubleshooting FaceTime
Use your Apple ID to register and use FaceTime. FaceTime registration validates your Apple ID and email address for use with FaceTime.
If you are unable to activate FaceTime, try the following:
Sign in to FaceTime for Mac using a valid Apple ID. After you validate the email address for use with FaceTime, other FaceTime users can connect to you using that email address. If you encounter issues registering or using an Apple ID account:
- Ensure that you have an active Internet connection.
- Verify that you are using a valid Apple ID at appleid.apple.com. You can also create an Apple ID or reset your password from this website.
- Check that your email address is verified in FaceTime > Preferences.
- If FaceTime > Preferences shows your email status as "verifying," follow the instructions in the verification email that was sent to complete the process.
- Toggle FaceTime off and on in FaceTime > Preferences.
- If still unable to Sign In follow the instructions in FaceTime, Game Center, Messages on OS X: Troubleshooting Sign in
You can make FaceTime calls using the FaceTime app. You can call FaceTime users whose contact information is in Contacts. You can add contacts and edit contact information in either FaceTime or Contacts. To place a video call, you may use a phone number or email address.
If you encounter issues making or receiving FaceTime calls, try the following:
- Verify that FaceTime is enabled in FaceTime > Preferences.
- If the issue persists, or if you see the message "Waiting for Activation", try toggling FaceTime off and then on.
- Verify that the Date, Time, and Time Zone are set correctly:
- From the Apple () menu, choose System Preferences > Date & Time > Date & Time.
- Enable "Set Automatically".
- Click the Time Zone tab and confirm the closest city is correct.
- Verify that both parties are connected to an active broadband Internet connection.
- See Mac OS X: Troubleshooting a cable modem, DSL, or LAN Internet connection.
- Consult Using FaceTime behind a firewall for necessary ports to open in firewalls, security software and routers.
- If you encounter issues using a Wi-Fi network, use standard Wi-Fi network troubleshooting to resolve interference and other issues.
- Verify the phone number or email address being used is the correct one activated for FaceTime.
- You can verify that you are using a valid Apple ID at appleid.apple.com. You can also create an Apple ID or reset your password from this website.
- Verify that both parties have installed the latest software updates for their Mac and/or device. See:
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