What skills and equipment do you have? Are the experimenter isles of Radio Shack places you've never visited?
Turning something on when another circuit is broken requires a logic inversion. A relay, a transistor switch, an integrated circuit can all be used but this maybe more than what you are actually being asked to do.
Figure out if you can simplify the problem by using a switch that is open when depressed and closed when released. This would allow you to use a much simpler circuit that has a battery and the switch and a light all in series.
http://www.1728.com/project2.htm has a burglar alarm diagram.
What parts are available at school? Have you talked with the teacher for recommendations on where to get parts to use?[/url]