Well you certainly require an anti-virus of sorts, especially if you are doing online banking. Don't format anything yet - lets first have a decent look at whats going on.
Follow these steps in this order:
1. Firstly, ensure that Norton is completely uninstalled. Look at option #24
here: AV Uninstallers
2. What anti-virus software do you currently have on your system? If none, I suggest installing free MSE
, and then performing a FULL
3. Post the output from that scan so we can be sure your system is clean.