How can I get the Leopard welcome video to play every time I turn on?

You may have to see if there is a way to use a utility such as Pacifist to
extract the portion(s) of the OS X 10.5 install-restore disc which has this
'setup assistant' which will separately from a full install, allow one to do
a less drastic intervention and lets a user change the user name and
address from the first startup sequence. I have not tried it, but this is a
way to try and get the part of that setup assistant that can be run again
and not affect the entire installation.

That does play the sound and the splash screen intro each time it is run;
and evidently that file can do it without needing the entire OS X installer
running (since it does so after the full install and before the personaliza-
tion process; plus can do it later on demand.) If you can find out how to
run the item and make a script of it, perhaps a script could be made to
just run the video/audio and not do the original intended deed again.

Finding out how to re-run the installer's setup only is easy, the rest isn't.
Be sure, if you follow this path, to note the pitfalls and do not run the
setup assistant itself if you do manage to get Pacifist to extract enough
of it to see about gaining access to the parts you think you want.

There are other thoughts on this topic I've had while keyboard it as I
think about it; and so at this point, I will say it is not quite ready for
prime time and would require investigation to learn of a process first.

A script could be built from some extracted bits and made to run on
startup, but not sure how complicated all that may be. Easier if you
can find the correct 'setup assistant' files and co-opt them...

{Took awhile to write this; perhaps the suggestion by V.K. above
may be a workable one, not requiring a lot of extra efforts.}

Good luck & happy computing! 🙂

there is no need to extract anything from anywhere since you have that movie file already. all you need to do is add it to the login items. this will open the movie on every login. to make it always open in full screen use this link
http://www.macosxhints.com/article.php?story=20050430024234333

Adding things to your login file in the user account
(admin or other that you have and use daily) is not
so difficult to accomplish. The general concept is
covered in my first post and probably in more detail
in your system's Help viewer, as seen from the main
Finder Menu bar in your main computer window.

A basic search there will give you options and of them,
some show a simple tutorial on how to get into and
change or add to the user account; as I said at first.

{Using Automator to watch movie files full-screen is an
almost perfect path; the link provided above is one of
the likely better ways to accomplish this yourself.}

And, there are ways to change the system from Console
and use the power of the system behind the GUI, too.
That you don't feel comfortable learning the rest of how a
system works is no big deal, I'd prefer the easy way, too.

So, there you have it. Oh, look... a white rabbit!
Good luck & happy computing! 🙂