If it were my machine I'd reinstall the OS entirely, but if you want to try to rip it out by hand and hope you catch everything you can try online virus scanners or tools like hijackthis, superantispyware, malwarebytes etc.
As for why norton didn't catch it, that's hard to say exactly, but new viruses are put out all the time, and old ones are repackaged in clever ways so while eventually most antivirus programs will update to catch the most common attacks there will be times when you are vulnerable even with antivirus software running. Once your machine is compromised it can be hard for your antivirus to see what it needs to. For example, Norton can ask Windows for a list of every file on your computer so it can scan then, but because windows is now infected it can lie and never tell Norton about infected files on your machine. Norton won't catch anything but you are still infected.
AV software run from a live CD, bootable USB stick, or by mounting the hard drive on another computer (one set up just to clean virus infected drives) can catch those types of problems by not depending on the infected operating system for information about your hard drive and it's files, but unless you're dealing with virus issues all the time the investment in time and effort for those types of solutions aren't really worth it in most cases when a re-install will be faster.
A periodic reinstall can be a good thing anyway. You get the benefit of a clean system that runs like new and it forces you to review what you actually need installed etc. Just be sure to carefully back up your data and make sure you scan your backups for problems once your system is back up and your AV software reinstalled and updated.
Some additional advice: once you know what virus you have, you should research it a little to see how it spreads so you can avoid it in the future. Follow best practices when it comes to things like not opening attachments from strange emails, use an ad blocker in your web browser at all times and (if you can) disable java-script by default with something like noscript for firefox, also use anything other than adobe acrobat for 99% of the PDF files you view (the ones that don't involve forms for example). that should go a long way to help keep your system clean
