If you're looking to purchase some security software, I would say go with one of the following:
BitDefender Internet Security
Trend Micro PC-cillin Internet Security
Panda Internet Security
E-Trust Internet Security
Haven't used BitDefender, but I have heard it's great.
Trend Micro is good, not that processor intensive.
Panda is good, but processor intensive- need plenty of RAM
E-Trust is good too, not that processor intensive.
There's just a few suggestions. You do want to get rid of Norton just as soon as possible.