Make sure this setting is not checked...
[ ] Remove programs if they are added by other applications
It's worth noting that Norton has finally given what seems to be a decent uninstall tool, for many of their products, I just used it today. You can just put symnrt.exe into a search engine, (or 'Norton removal tool' or similar phrases) always make sure you are downloading from a reputable site, like symantic itself, or majorgeeks, or whomever.
You may like Norton, it which case this is just for note, however many folks feel that it is far to obtrusive, aggressive, resource-hogging and hard to deal with (also a target itself due to the number of machines it installs on). They install too deep into the operating system, making compatability issues for many programs. You could say in rootkit fashion.