Norton monitors everything and disables security centre (it asked me if it was okay first) to avoid duplicate error messages. Mine is disabled too, I use Norton Internet Security 2008 myself.
I don't know what problems you'll cause if you turn it on, so on your head be it...
Click Start > Run and type services.msc
Scroll down to Security Centre and double-click it. Change startup type from Disabled to Manual for now, then click the button labelled Start just below. If everything is okay, you can set it to Automatic, but I bet Norton will complain.