As long as you are behind a router (which provides a hardware firewall), and you have Windows Firewall enabled, you should be fine. I would go ahead and disable the Symantec one (better yet un-install it if possible) and leave it at that. The combination of the hardware firewall and the Windows Firewall will provide adequate protection for you.
I do want to draw your attention to this post however:
Not to freak you out or anything, but it is worth looking into. Consult your specific router documentation on how to change the user name and password.
Let me know if you have any other questions or problem.