AKICOLJ: Photoshop (CS5)

This should be really easy, but it's not. I have an image. The item in it is distinct enough from its background that selecting the part I want to keep is easy. I've done that part, although I had to cut the selected part and paste it into a new document (inverting the selection and hitting delete did nothing to get rid of the background no matter what the directions say). But now I've apparently got a zombie background. It won't GO AWAY. I can't make it go away no matter what I do. I get it to where it looks like it's gone in Photoshop, and prints in Photoshop like it's gone, but when I take the supposedly cropped version and place it in an InDesign document, the background looks like it's gone on the screen, but keeps magically reappearing and screwing everything up when I print it.

Help? Please? The mood icon does not begin to describe my sentiments at the moment.