Hello alexfrommilton,
Thank you for using Apple Support Communities. It's my understanding you're unable to active iMessage and FaceTime when using your Apple ID. I use these apps almost daily. I'd be concerned if I was unable to activate, especially if a different Apple ID works fine. I am happy to help.
First, I recommend trying the steps below.
- Go to Settings > Messages and turn off iMessage.
- Go to Settings > FaceTime and turn off FaceTime.
- Restart your device.
- Turn iMessage and FaceTime back on.
If you get an error when trying to activate iMessage or FaceTime
Also, go to the Apple ID link below. Sign in with your Apple ID and confirm all information is correct.
Apple ID
Have a great day!