To get something to run
after you've logged into the GUI you need to use the desktop environment's autostart feature. If you're using KDE (default in Mandriva) then try the ~/.kde/autostart folder, in GNOME I think there's a GUI for adding things to be autostarted. More info:
http://gentoo-wiki.com/HOWTO_Autostart_Programs
http://mail.gnome.org/archives/gnome.../msg00142.html
The acutal script itself will just be a text file, just like .bat files in DOS. However you have to do 2 things to make it a valid script:
1) the first line should be
to tell Linux that its a bash script, bash is the language of the default command line.
2) you need to right-click->properties on the script file and set the permissions to be executable, or use the chmod command from the command line.
Now to actually play the video file you'll need to use one of the video players, eg. totem or kaffeine or mplayer from the command line. I'm not sure about kaffeine or totem but I know mplayer has a lot of command line options (man mplayer) so there should be a way to get it to start in full screen mode.