Firstly - did you remove Norton properly? You need the Norton Removal tool:
http://service1.symantec.com/SUPPORT/tsgeninfo .nsf/docid/2005033108162039
If you don't it may be conflicting with your new firewall causing no end of problems. Don't be tempted to reinstall Norton - it is more trouble than it is worth.
Your trojan needs to be got rid of. Without knowing which trojan it is, we will have to run several programmes to try and sort it out.
I am assuming you have Windows XP.
Download and run A2:
http://www.emsisoft.com/en/software/free/
And AVG anti-spyware (it used to be called Ewido):
http://www.ewido.net/en/
Both of these programs are free.
I would recommend Comodo as your firewall:
http://www.personalfirewall.comodo.com/
Avast as your Anti-virus
http://www.avast.com/eng/avast_4_home.html
And spywareblaster which runs in the background as extra protection:
http://www.javacoolsoftware.com/spywareblaster .html
All of these are free. Consider installing them when you have got your trojan sorted.
If you are still having problems, I will try and walk you through running them again in safe mode. :)
Good luck.