Minecraft multiplayer not working?

I know nothing about these things so bare with me!
My kids have minecraft for the xbox 360. Its the actual disc not the downloaded version.

They got a new xbox for Christmas and now multiplayer won't work. When both of them are signed into xbox live they can't get minecraft to work in split screen 2 player mode. It won't work either when one invites the other. The game still lets them play online with their friends but they can only play one at a time!

The xbox is connected via hdmi cable.
Any help is greatly appreciated!

A HD (High Definition) TV is needed for Minecraft XBOX360. If you do not have this, then they can't play together.
Ajax