My problem is with a Mitsubishi LCD-projector - model SL1U - that will
not display movies played on my laptop.  I am able to hook it up to
the computer just fine, and my laptop's screen is projected on to the
wall just fine.  However, even though the movie plays on my screen,
and although the window in which the movie is playing is projected
onto the wall, THE MOVIE DOES NOT PLAY ON THE WALL.

I've tried changing the resolution, but it does not affect the
outcome.  Everything else is working just fine -- I can open and close
programs, urf the internet, and even play flash animation.  No matter
what I try, though, I can't get my movie to play.

It's connected using a VGA cable.  When I hook it up to my dvd-player
using those triple Red-White-Yellow cables, it plays the DVD just
fine.  Please, somebody, tell me how I can make this work?

I've had that problem before using S-Video output on my laptop to a TV
(same thing as a projector to a video card, basically).  The problem
is NOT with your projector, but in how you're displaying your movie.

Are you running the projector as a second monitor, or as an extension
of your desktop?

I remember that when I tried to display a movie on both the laptop
monitor and the  TV, it didnt work.  If your video card is like mine,
it can only display a DVD on one or the other, not both
simultaneously.  Try setting up your projector as an extension of your
desktop, drag the movie player window over to the projector screen.  I
know this sounds weird, but make sure ALL of that movie player window
is inside of the projector screen.  If all of it isnt completely in
the projector window, you will see all black on the projector screen. 
Then I can maximize it and it usually works fine and looks great.

This setup is the only way I could get the TV (projector in your case)
to display a movie.  However, my laptop monitor goes black when I do
this, but like I said, the movie looks great on the TV screen.

Basically its like this in a nutshell: If you maximize the DVD player
window on the laptop monitor, you get the movie on the laptop and
black on the projector. If you drag the movie to the projector and
maximize there, you get movie on the projector and black on the laptop
monitor.

Hope that helps, it worked for me.

Try starting the movie using the player ( File > Open ) AFTER you
start projecting the image.