Chunk, if you examine p.2 of your 1500 manual you'll note that one of the features shows a double-ended arrow between Composite and S but a single-ended arrow going from S to Component. This strongly implies that transcoding from S down to Composite is possible, but not from Component down to S(or Composite). For more than a strong implication go to p.17 and note that the signal flow chart there shows that there's no flow down to either S or Composite from the Component input.

I'm not familiar with the requirements of the xbox, but if you've described them correctly you can't make that connection with your 1500 and TV.

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Enjoy the music, not the equipment.