Thanks for the quick response, Dave.
In another thread someone had suggested that “Render with OpenGL” be turned off. I had it turned off, so I turned it on. Viola.
I actually tested it both ways, and on my setup OpenGL needs to be on for the videos to be rendered from inside the pre-comps.
However, that is great advice about actually deleting unused effects. It could significantly improve the render speed, if there are a lot of invisible effects hanging out.
Thanks again,
Elliot