Have you tried using "Last known good configuration"
or, if you think norton has indeed got installed, what about using a "System restore"..
Since something is installing norton without your express permission, i would recommend three things:
a) check what all is there in the 'start-up' list, using Ccleaner. Disable/delete anything suspicious scheduled to start up with system start.
b) full scan with Avast
c) full scan with Malware Byte Antimalware (MBAM)