To solve the problem I have an A/V switch. It's not an uber-expensive one, but it gets the job done. And usually I'm putting stuff like the PS2 on the switch, so top-notch video quality isn't required.
I hadn't been using the switch (largely because I couldn't find it after the move...) In order to get the LD player into the system I pulled the switch out and plugged the LD player and the PS2 in. The LD player feeds the signal through fine, but the PS2 won't go through.
I thought maybe the other ports on the switch were dead (even though they were working before the move...??) , but even when I plug in the PS2 on the port that the LD player is using, the signal won't come through. I've tried a bunch of other things (the other PS2, the TiVo), and only the LD player works.
Does this make sense to anyone? Is there something different about the video signal for the LD player that it's going through okay while the other video inputs don't? This makes no sense to me...