Generally, you remove applications by using the Windows utility for the task, but Norton Antivirus tends to get in a bit deeper into the system, so it's tricker to remove it completely. Here's how you can do that:
1. Go to Start --> Control Panel --> Add/Remove Programs.
2. Scroll down to your Norton program
3. Click Change --> Remove All.
You will be asked to restart your PC. Do so.
4. Now go to Start --> My Computer --> Program Files. Right click on each Symantec folder and select Delete.
5. While you are in Program Files go to the Common Files folder at or near the top of the Program Files window. Delete every Symantec folder there. And, again, restart your PC.
6. Go to Start --> Search --> All Files and Folders --> More Advanced Options. Check each option except for "Case sensitive"
Now type in Norton and delete each Norton folder from the search results (Again, right click, choose "Delete"). One more time, restart your PC.
7. Repeat step 5 except type Symantec in the "Search" box.
The next step is trickier: go into the Registry.
1. First thing to do is Back up the Registry. I'll be saying more about the Registry later. But suffice it to say that the presence of uninstalled security software in the Registry can conflict with newly installed security software and cause system freezes. So can folders of "uninstalled" programs for that matter.
2. Once again, go to Start, then click on "Run". Type in "regedit"
3. Go to the top of the Regedit window. Click (+) next to HKEY_CURRENT_USER. Go down the thread until you see Software. Click on Software and scroll down the thread until you see Symantec. Right click on Symantec and choose "Delete".
4. From there go down to HKEY_LOCAL_MACHINE and repeat step 3. Restart your PC.
5. Click (+) next to HKEY_LOCAL_MACHINE, now: Click (+) next to Software, Click (+) next to Microsoft, Click (+) next to Windows and Click (+) next to CurrentVersion.
6. Select the Run folder. Right-click and delete each Symantec entry you see (if present). Restart your PC.
That should completely eradicate Norton Antivirus from your system!
Note: Symantec offers an uninstaller for NAV (Norton Antivirus) 5.0/2000/2001/2002/2003 which they say removes Norton from your Program Files and the Registry, but commentary on various discussion boards suggests that it might not work too well.