Hi,
When you say that you took out the fuse, did you mean Fuse #43 in the engine bay fuse block?
Have you tried replacing the Horn ''relay'' (Relay #21) in the engine bay fuse block, with a similar relay found in the fuse block (if there is one) to prove that the relay is not the problem, instead of the horn button.
Here is an image of the engine bay fuse block taken from this [http://www.autogenius.info/pontiac-grand-am-2001-2004-fuse-box-diagram/|website] showing the location of the horn relay (red) and the horn fuse (purple)
[image|1351714]
(click on image to enlarge for better viewing)