Just so I understand you...
So you're trying to install iLife, but the disc keeps ejecting when you put it in your computer. You tried calling Apple, but Apple said that the warranty (AppleCare) on your computer had run out. I'm not sure what Leopard has to do with it, but there could be a problem with your computer's disc drive. Are you sure your computer should be out of warranty? AppleCare is three years long, remember. Did you just not buy AppleCare? Or did you buy it and never registered it? There's a lot of little questions about AppleCare that are important to check before calling it quits.
So the problem is either with the disc drive or the iLife disc itself. Try putting the iLife disc into another computer and see what happens. You could consider picking up an external disc drive (~$70). You could also try copying the iLife disc to a flash drive, and then installing iLife via the flash drive. But to do that, you need access to another Mac.