Two possible problems come to mind.
1. Jack color coding is not alway standard. Check the labels on the jacks themselves.
2. As you said, "new Sony DVD Changer isn’t able to output 480i from the component jacks." The Toshiba LCD is able to accept a 480p signal, but the old JVC cannot. The Time Warner box has a component video out, but it is probably not 480p. Not all component video outs are prog scan.
1. Jack color coding is not alway standard. Check the labels on the jacks themselves.
2. As you said, "new Sony DVD Changer isn’t able to output 480i from the component jacks." The Toshiba LCD is able to accept a 480p signal, but the old JVC cannot. The Time Warner box has a component video out, but it is probably not 480p. Not all component video outs are prog scan.