If it is a company owned computer, you better check with your ITech at work.
If it is your laptop, wait until the coverage for Norton runs out then think of using one of the free AntiVirus programs out there like Avast, Avira, AVG.
If you are using Vista, the Vista firewall is a good two way firewall, WinXP firewall is only one way and not good.
The free AV utilities are good and use much less resources than Norton and less problems with stuff getting by.
You just have to remember to update it every couple of days (in most cases, they are not automatic (price to pay for being free)
You should also, download, install, then update SuperAntiSpyware to keep your computer free of those nasties and run it every week or so, another good one to have is SpywareBlaster which runs in the background and stops the adware from loading. Again, make sure that they are updated periodically.
P.S. When you finish with Norton, make sure it is completely uninstalled before putting one of the free ones on. You cant run two AV programs at the same time