My computer is invected with trojans, cookies and other harmful virus's. What should I do?

Personally I would stay with Norton. It is a pretty good virus scanner, especially if you don't have permissions to change it. Let Norton run it's scan and get rid of everything for you. That other Antivirus program that is supposedly running is probably a virus, try to harm your computer, that's why Norton is telling you that. Get that other program deleted through Norton, or atleast Quarentined.