Big picture:
1) what version of Norton do you have, hopefully one of the modern ones (2004 or 2005), since that appears to be your real-time protection here. If you want, you can grab a free 15-day trialware of Norton Antivirus 2005 from
here. Run LiveUpdate repeatedly, rebooting as prompted, until it comes up happy, then tack on the daily
Intelligent Update.
2) is Norton set to use maximum heuristics and to scan within compressed files on both the AutoProtect and the Manual Scan panels in Options; if not, change that.
3) patch your system with the latest Microsoft updates.
Microsoft Baseline Security Analyzer is a good tool, it sees deeper than Windows Update does.
4) right-click My Computer > Manage > Users & Groups > Users, and give all the Admin-class accounts a strong password such as
dragonic@AT to prevent a no-brainer appropriation of the Admin-class accounts' powers.
5) if you have a router, close the ports you don't need open. Ones you'd probably need open include 20 & 21, 25, 53, 80, 110, maybe 143, and 443. If the computer comes down with another remote-controlled Trojan but can't "call home" to get instructions because the router is blocking port ____ outbound (insert random port the Trojan wants to use), that's partial damage containment at least.
5) be more careful

This stuff doesn't fall from the sky. Warez, pr0n, P2P and letting other people use your computer are all potential risk factors that are under your control. If others will be using your computer, make sure there's a Limited-class account without password protection for them to use, and protect the Admin-class accounts. Consider using Limited yourself, they're harder to exploit.