Apple ID & Facetime not in sync

My Dad updated their iPad to iOS 8.4.1. Around that time FaceTime stopped connecting. Somewhere along the line he had to change his AppleID password. (It's possible other things were changed that I'm unaware of.)

Now, they cannot connect to FaceTime or Messages on either their iPad or MacBook Pro (OSX 10.7.5). We can connect to the App Store, iTunes, & iCloud using the Apple ID without any problem. Also, using either of their devices I can connect to FaceTime using my own Apple ID. And I cannot connect with their ID using my own iPad.

I noticed on the iPad under Settings > FaceTime there is no on/off toggle now like in older iOS versions.

I've seen people post the same question here and the answer is always to make sure Date & Time is set to automatic. It is. And I have reset the iPad. But since the problem appears on both devices, and other Apple IDs work, it seems to me the problem is somewhere outside of our control.

Thanks for any help you can give me.