Symantec makes the Norton products. So it sounds like you have the Norton AV 2005 and are trying to update to 2007. Since 2005 is now considered the 'old version', I guess that's why you need to uninstall it, then install 2007.
That is too funny about the "symantec" password! Never heard that before. I also haven't heard of a security program requiring a password to uninstall!
This is a must though and you may have to do it in Safe Mode:
Stop Startup for uninstall:
You will need to make sure though that it does not start when you boot, or it will not allow the uninstall:
Start> Run> type in ''msconfig' without the quotes> Selective Start-up> Startup tab> uncheck the process that is for this> Apply> OK.
Reboot> Close the nag message that comes up after checking 'don't show this message again'.
Now try the uninstall in the Control Panel> Add/Remove Programs.