http://www.lg.com/uk/home-entertainment/lg-BH6220S-home-cinema-system shows this has a composite output so it is possible that the player is set to use that.

Why 3D BD works is that said content will never display over composite so it may autoswitch to HDMI.

Page 20 of http://www.lg.com/lgecs.downloadFile.ldwf?DOC_ID=KROWM000357763&ORIGINAL_NAME_b1_a1=Europe_%28United_Kingdom%29_BH6000_Series_ENG.pdf&FILE_NAME=KROWM000357763.pdf&TC=DwnCmd
could mislead many.

Page 21 however shows a reset and I'd be sure there is no composite lead connected.
Bob