I just purchased Illustrator CS5, and can't get any of the .ai files to open. I've downloaded all of the necessary viewers.
Do you get any errors? Are you able to create a new AI document?
Moving this discussion to the Illustrator forum.
Can you postr a file to a remote server so we can download it and see?
It sounds like the files are locked or you moved them from a school server to your home computer but need to change the permissions.
Just a guess.
Also make sure the students files are CS5 or older.