Q: Restored Apple TV 3 will no longer connect to Bluetooth.  When setting up does not go past Activating screen.

Are you sure you are not confusing using your Mac to assist setup with this?:

Use an iOS device to set up your Apple TV (3rd generation) - Apple Support

Don't think you can use the Mac.  You need to pick the manual setup option.

The 3rd gen only accepts bluetooth keyboards, the only connection to the Mac is through home sharing and airplay, and when tethered for restore.

If you are stuck on that screen it means you are not properly connected to the network.

If on wifi try ethernet

Reboot ATV and router

Make sure router has port 123 open (refer to manual if unsure)

Test on another network