Revo Uninstaller might be able to uninstall it:
http://www.revouninstaller.com/
Use the "Moderate" or "Advanced" function.
Symantec has a web site that shows how to
manually uninstall Symantec Antivirus:
Manually uninstalling the Symantec AntiVirus 10.0 client
There is also another page that will tell you more information based on your operating system:
Uninstalling your Norton or Symantec product
It involves manually editing the registry, so if you're not comfortable doing that, don't do it.
Sometimes you need to reinstall Symantec Antivirus in order to successfully uninstall it so this is something you should also try.
Here's a link that tells you how to uninstall it without a password, if that is the problem:
Unistall Norton Network Antivirus Without a Password | Owen Consulting - IT & Web support for Small Buisnesses
Symantec used to publish an "universal uninstaller" that would remove everything, but I don't see it on thieir site any more.