Connection Z to Internet

Here are the major problems, I have been barely able to connect the Z so i can tcpip AND ping my computer, but no internet.

I made another post, there are the exact specifications of how my network is operating. To restate it to be one post, 192.168.1.1 is my gateway, 192.168.1.100 is my router i believe, 192.168.1.101 is THIS computer, 192.168.1.102 is another computer on my network...

Do i have to force my Z to be say 192.168.1.103?

If you explain it, preferebly explain it as simple as possible because niether of us has any experience in network management. Anyways I read on a much older post about setting up a network but that only worked to an extent, added some ip numbers to hosts file and another one not sure of name off back of my hand.

I am not rulling out of a possibility that the built-in-firewall in my router could be the cause of this, is there a way to test? Is there a way to temporaraly disable? I am running off a Linksys BEFW1154 or BEFW11S4 - cant tell the numbers appart that well (the S from the 5) i need glasses . I think its an S

Thank you for your patience with this.