Sounds like your disk has a problem that even Norton Utilities can't fix. It's rare, but it happens. If this were my computer, I would buy a copy of DiskWarrior from AlSoft. You can get it at CompUSA or Fry's 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 of reindexing these directories. A good indicator that it's time to rebuild is if your documents revert to generic-looking icons. This means your Mac can't remember what program opens that document and is a hint of a damaged desktop directory. Mac users can rebuild their desktop files by holding down the Apple and Option keys and rebooting.