In case anyone else has this problem - quite a few of the games we got (Halo 3, Pure, Tomb Raider: Legends, etc) wouldn't work in 50 Hz display mode. There's no warning about this on the XBox packaging, even though onme of the games that come in the box (Pure) has this limitation. The standard composite video cable that comes in the box seemed unable to work with our TV (Sony Bravia) in 60 Hz mode.

I just went out and bought an HDMI cable and this has fixed the problem, but be warned - if you have a TV without 60 Hz capability you can't play all the games.