Yes, yes and, well, yes.
Are the lines rolling or still?
You mentioned that the lines appear only via component cables. Can you try an hdmi, or even s video cable?
Bottom line, I would determine the cable issue first by isolating them (components), and then trying hdmi (or s video if you have one laying around). In this way you have eliminated cabling and connections.
Once you've determined that it is neither a cabing nor a connection issue, I would suspect it is then most likely be an interference issue (unless the lines are still, in which case it could be the projector itself). Let us know what remains after the process of elimination. Cheers.