Sounds like your disk has a problem that even Norton Utilities can't fix. It's rare, but it happens. I would buy a copy of DiskWarrior from AlSoft. You can get it at major electronics retailers or online at any good software store. DiskWarrior is a repair tool for your Mac's directory files.
All computers keep track of everything through directories.
The Mac keeps track of which programs can open which documents, which documents are in which folders and where the folders are in these directories. Rebuilding the desktop is a way to reindex these directories. It's like telling your Mac to take an inventory of all files and folders to make sure it knows where everything is. A good indicator that it's time to rebuild is if your documents revert to generic icons. This means your Mac can't remember what program opens that document and is a hint of a damaged desktop directory.