Hello Marmalady,
Thank you for your question. It sounds like you are not able to sign into FaceTime on your comptuer. I found this article to help you troubleshoot what you are seeing named
FaceTime for Mac: Troubleshooting FaceTime
http://support.apple.com/kb/ts4185
Start with these 2 sections and proceed to the troubleshooting section in the article if needed:
To participate in video calls, your Mac needs:
If you have multiple cameras or microphones attached to your computer, use the Video menu to select the camera or microphone you wish to use with FaceTime for Mac.
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:
Thank you for using Apple Support Communities.
Cheers,
Sterling