home network

I can not access the wireless home network I am trying to set up from my Inspiron 8200. My Dell 4700 desktop is the host and I can  ping its IP address and the gateway and DNS addresses. The Inspiron will ping the gateway, but not its own IP address nor the DNS addresses. MY host does not recognize the Inspiron as a computer on the network. I switched the host adapter to the Inspiron - no improvement/changes in pinging addresses. I have gone through Microsoft's trouble shooting protocols without success. Can anyone help?