Some advice regarding recovery issues and using my Norton Security Suite

I am pretty certain I have some kind of virus/malware/hacking issues in which no matter what application/program/recovery I use, it is reading that it has been installed and the problem corrected however when I re-boot the problem is still there.  Whether it is virus/malware related and even when I attempt to do a system recovery/re-install.  I even have problems with my router login's and password security.  Is it possible to have something in my bios, start-up, ini, registry, placed by someone which allow the programs/applications to install, then they are un-installed once I've rebooted, including my Norton protection. I had to manually get to the Norton site here because I got redirected from clicking in my Norton Security Suite.  Any assistance will help.

 

I can attach the url I was sent to if any1 is interested.