Is it possible you have two Norton applications installed?
I refer to the OP where you said you downloaded the latest one to take over from the free one that expired.
Couple of points: - The "free" one wasn't actually free; it was a trial version, as installed on many new out-of-the-shop units. Once the trial is up, you have to pay Symantec some $, they will send you a license, you enter the license and hey presto, your expired unit is alive and well.
- If you actually downloaded a new Norton (which might well be a different program to that installed) without removing the trial one, they will fight and squabble, and hog computer resources. Almost anything is possible.
From reports I've seen, the latest versions of Norton are a heck of an improvement since 2010, being a lot lighter and cleaner. Not for everyone, but for many. Personally I've been put off Norton because of it's past problems, and I don't really like the way they do business - my preferred alternative is Avast free, and it has never given me a reason to want to change.
Whatever AV you are installing or removing, there is more often than not a specific removal tool designed to finish off the removal. It doesn't always find leftovers, but often does, and is therefore worth running.