Anytime is a good time to dump Norton. It can, and often does, cause all sorts of problems. The difficult part will be getting rid of all vestiges of the thing, but you should before installing any new one.
Do the “Add or Remove Programs” in Control Panel and reboot. Then go to Win Explorer and delete any of their folders. Then do a search for “Norton” and delete all instances. Then do another search for “Symantic” and delete those. Reboot. If you are lucky, it will be mostly gone.
Unfortunately, there will probably be a mess of Norton entries in the Registry. You can remove those also, but ONLY if you are experienced in messing with the Registry, back it up before (and also do a Restore point), and know what you are doing.
As has been mentioned, AVG, Avast and Kaspersky are all very good free programs. Yeah, you do have to search hard on the website now to find the free version of AVG, but it is worth it.
Finally, if you want to buy a program, I’ve used Trend Micro’s PC-cillin for several years and it is very good without taking over your whole computer. You have a lot of choices in tweaking it and picking what features you do or do not want to use.