Your problem is not that you need to convert it for usage on another computer... you have to finalized your video in Windows Movie Maker first by Publishing it.
The reason you can't play a WMM (Windows Movie Maker) Project on any computer but your own, is because that is where the source files contained in your project are located. That is why you have to Publish it first.
To Publish your video in WMM, make sure the movie is in the program, then:
> Click View and Tasks to bring up the task pane
> Under Edit, click Publish to ----- this computer
> Name the video and select a destination to save it to (desktop is best for easier access/preview after publishing...move it later)
> Click Next
> Select: Best quality playback on my computer (recommended)
> Click Publish
When the video is published, locate from wherever you saved it to. Click on it and it should open in your default media player. If it plays, then it has been finalized. Now you can play it on a media player, email it, upload it or burn it to CD/DVD.
You can even copy it to your Jump/Flash drive to take and use on another computer, like the one at your school. Just remember... the final step in creating a video with WMM (Vista or XP) is to Publish it.
If you want more helpful hints, how-to articles or informative tid-bits on WMM, visit my Blog at:
http://wandawonderswhy.blogspot.com/search/label/Windows%20Movie%20Maker
I'm sure you'll find some interesting items there. Good Luck.
:)