I wouldn't personally go near Norton. Myself and members of this community would always advise to go with the "Free Software" Which does exactly the same principle of the dreaded Norton. With Norton it Slows Down your computer.
To Remove Norton 2008 Goto this link and run the tool to remove Norton 2008 from your computer:
Next Step Go Over to here: click here
Some Combinations to go with are:
1 Antivirus which can be either:
AVG Antivirus or Avast Antivirus
Either Zone Alarm or Comodo Firewall.
I use here Avast and Comodo.
The Next you will need is some good Spyware Protection:
This is what I use:
Spybot Search and Distroy
This more than enough for me.
If you need any more help come back to us.