Do I Need To Run A Software Firewall On 2nd PC ?

[308nato]

My dear old ma uses a wireless ISP. They run a hardware firewall to keep people out from the "outside". She uses a sofware firewall on her pc which is running XP. I am going to set up an old box running 98SE with a simple nic>nic internet connection sharing/printer sharing network. She's tired of pop messing up her computer and wants him to have his own.

Is it necessary to run a software firewall on the 2nd pc if there is one running on the internet "gateway"?

Sorry for the basic ?? but I have no idea how this kind of thing works. Thanks.