Program with questionable value in use

I use Norton Internet Security already for several years on a Windows XP system, and although I use the PC alone, I have set up two accounts, one with and one without administrator privileges, which I almost exclusively use the latter. So I imagined myself with a firewall and a restricted account in safety until I caught my Delta Homes virus. Previously, I have noticed that in the All Programs list different programs frolicked, I had never installed. In addition, repeatedly appeared Windows messages that this or that application need administrator rights, ie Norton would not have prevented the installation of these intruders, I would not have been logged with a limited but with an administrator account.
To make it short: The purchased program has neither the infiltration of more or less malicious software prevents even brought their disposal access routes. This was achieved only through the free software AdwCleaner. To my absolute amazement, how much digital dirt has crept on my firewall over. When I bought Norton for the first time, it ranked in the most test reports yet in the first place. But that is long gone.