network and firewall questions

[Andrew L. Gould]

I'm still very much a newbie regarding networking issues and firewalls; so if 
I need to be slapped, please be gentle.  ;-)

Most of my home computers are behind a NAT router with very simple firewalls 
-- let all requests out, allow established in, deny everything else.  I put a 
test computer in the DMZ the other day to experiment with firewalls, and 
remote access as I travel next week.

Can someone access your computer by a port if nothing is listening to that 
port?

If not, then if you turn off services that you don't use and need to access 
used services remotely (i.e. let them through a firewall), do you need a 
firewall?

Thanks,

Andrew Gould